# All (96,20,4) difference sets. # This file creates a list 'DS96' in which DS96[i] is a list # of all inequivalent (96, 20, 4) difference sets in the group [96, i]. # (Exception: if the chain length is 5, we might not have ALL of them.) # This list is exhaustive with the following possible exceptions: # Groups 64, 70, 71, 72, 227 have difference sets but chief series of # length 5 and BruteForceSieve takes too long at this point... # Groups 218, 220, 230 and 231 have large automorphism groups and # an exact list of inequivalent difference sets is still difficult. # This file has 2607 inequivalent difference sets # (as of May 20, 2006.) # Groups of order 96 with difference sets: list := [ 10, 13, 14, 20, 41, 51, 52, 54, 64, 68, 70, 71, 72, 75, 77, 78, 79, 83, 84, 85, 86, 87, 88, 90, 91, 92, 94, 95, 96, 97, 98, 99,101,103,105, 129,130,131,133,135, 136,141,142,143,144, 145,146,147,151,152, 159,160,161,162,164, 165,166,167,168,169, 170,171,172,173,174, 175,177,185,186,188, 190,191,194,195,196, 197,202,205,206,209, 210,212,218,219,220, 221,223,225,226,227, 228,229,230,231]; # 94 groups have difference sets, 137 do not. # Images of size 48: # No DifSet image: 1,2,5,6,7,9,17,23,29,36 (10 groups) # The other 42 groups of size 48 have (96,20,4) difference set images. # These 48-images rule out the 47 groups of order 96: # 1, 2, 6, 7, 8, 9, 11, 15, 16, 18, # 19, 21, 22, 23, 24, 25, 27, 28, 37, 46, # 48, 55, 59, 60, 66, 76, 80, 81, 82, 89, # 93,102,104,107,109, 110,111,112,115,116, # 127,132,134,137,176, 189,207. # Images of size 32: # No DifSet image: 1,18,19 (3 groups) # The other 48 groups of size 32 have (96,20,4) difference set images. # Images of order 32 rule out the 9 groups: 1,2,6,7,33,34,35,61,62 # The last 5 are NOT in the list of groups ruled out by 48-images. # Thus 52 groups are ruled out by looking at homomorphic images. # The remaining 84+1 groups are eliminated by Omar/Ken (2 methods, both exhaustive.) # Many of these by Omar, verified by Brute Force Sieve. chain_of_length_6:= [ 65, 66, 67, 69, 73, 74, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 226, 228 ]; chain_of_length_5:=[ 3, 64, 68, 70, 71, 72, 203, 204, 227, 229 ]; ############################################################ DS96 := [ ]; # Working on Small Group [96, 1]... # NO: [32,1] image; NO: [48,1] image DS96[1] := [ ]; # Working on Small Group [96, 2]... # NO: [32,1] image; NO: [48,2] image DS96[2] := [ ]; # [96,3] ruled out by BruteForceSieve on May 18, 2006. DS96[3] := [ ]; # Working on Small Group [96, 4]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[4] := [ ]; # Working on Small Group [96, 5]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[5] := [ ]; # Working on Small Group [96, 6]... # [96,6] has [48,7] image (so NO DS) # NO: [32,18] image DS96[6] := [ ]; # Working on Small Group [96, 7]... # [96,7] has [48,7] image (so NO DS) # NO: [32,18] image DS96[7] := [ ]; # Working on Small Group [96, 8]... # [96,8] has [48,7] image (so NO DS) DS96[8] := [ ]; # Working on Small Group [96, 9]... # [96,9] has [48,9] image (so NO DS) DS96[9] := [ ]; # Working on Small Group [96, 10]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 4 difference sets: DS96[10] := [ [ 1, 2, 3, 5, 7, 8, 9, 21, 33, 37, 38, 41, 54, 58, 65, 74, 75, 86, 88, 95 ], [ 1, 2, 3, 5, 7, 8, 9, 21, 37, 38, 51, 60, 65, 66, 68, 69, 74, 78, 81, 87 ], [ 1, 2, 3, 5, 8, 9, 12, 22, 27, 30, 37, 38, 46, 65, 68, 69, 74, 86, 90, 95 ], [ 1, 2, 3, 5, 8, 9, 16, 32, 37, 38, 48, 53, 57, 65, 66, 67, 73, 74, 76, 87 ] ]; # Working on Small Group [96, 11]... # [96,11] has [48,9] image (so NO DS) DS96[11] := [ ]; # Working on Small Group [96, 12]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[12] := [ ]; # Working on Small Group [96, 13]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 16 difference sets: DS96[13] := [ [ 1, 2, 3, 4, 7, 10, 12, 14, 23, 26, 37, 44, 48, 50, 60, 71, 75, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 34, 37, 44, 50, 60, 62, 75, 78, 82, 85, 94 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 37, 41, 44, 50, 60, 69, 75, 78, 85, 86, 95 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 37, 44, 45, 47, 50, 60, 72, 73, 75, 78, 85 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 37, 44, 50, 55, 60, 75, 78, 80, 85, 91, 96 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 37, 44, 50, 59, 60, 61, 75, 78, 83, 84, 85 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 37, 44, 50, 60, 66, 68, 75, 78, 85, 87, 88 ], [ 1, 2, 3, 4, 7, 10, 12, 14, 26, 37, 44, 50, 60, 75, 77, 78, 79, 85, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 12, 22, 24, 26, 38, 43, 45, 48, 60, 70, 78, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 10, 14, 22, 26, 43, 50, 55, 68, 69, 70, 71, 73, 82, 83, 92 ], [ 1, 2, 3, 4, 7, 10, 22, 24, 26, 27, 38, 43, 51, 57, 58, 69, 70, 71, 73, 88 ], [ 1, 2, 3, 4, 7, 11, 14, 28, 30, 44, 53, 56, 57, 59, 64, 65, 75, 77, 80, 94 ], [ 1, 2, 3, 4, 7, 11, 27, 28, 38, 44, 51, 56, 57, 58, 59, 65, 79, 82, 85, 96 ], [ 1, 2, 3, 4, 10, 12, 14, 26, 33, 50, 55, 57, 68, 69, 71, 73, 81, 82, 83, 92 ], [ 1, 2, 3, 4, 10, 12, 19, 21, 24, 26, 38, 44, 45, 46, 48, 60, 78, 87, 90, 95 ], [ 1, 2, 3, 4, 10, 12, 24, 26, 33, 38, 40, 43, 46, 55, 57, 67, 77, 81, 82, 83 ] ]; # Working on Small Group [96, 14]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 4 difference sets: DS96[14] := [ [ 1, 2, 3, 6, 8, 12, 16, 28, 30, 36, 43, 52, 59, 60, 61, 65, 70, 79, 80, 81 ], [ 1, 2, 3, 6, 8, 12, 21, 28, 30, 34, 36, 37, 40, 46, 52, 60, 81, 82, 91, 92 ], [ 1, 2, 3, 6, 8, 16, 21, 27, 28, 36, 46, 51, 52, 53, 62, 65, 75, 77, 94, 96 ], [ 1, 2, 3, 6, 8, 27, 28, 36, 37, 40, 43, 51, 52, 53, 55, 70, 75, 83, 84, 93 ] ]; # Working on Small Group [96, 15]... # NO SOLUTION at level 4 with normal subgroup 2 and quotient [ 48, 17 ]. DS96[15] := [ ]; # Working on Small Group [96, 16]... # NO SOLUTION at level 4 with normal subgroup 2 and quotient [ 48, 17 ]. DS96[16] := [ ]; # Working on Small Group [96, 17]... # Both BruteForceSieve (early May 2006) and Omar say 'NO'. DS96[17] := [ ]; # Working on Small Group [96, 18]... # [96,18] has [48,1] and [48,9] image (so NO DS) DS96[18] := [ ]; # Working on Small Group [96, 19]... # [96,19] has [48,9] image (so NO DS) DS96[19] := [ ]; # Working on Small Group [96, 20]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 8 difference sets: DS96[20] := [ [ 1, 2, 3, 5, 7, 8, 12, 19, 22, 31, 32, 35, 44, 45, 69, 74, 76, 78, 86, 89 ], [ 1, 2, 3, 5, 7, 8, 19, 22, 23, 30, 31, 35, 44, 54, 57, 68, 73, 74, 87, 90 ], [ 1, 2, 3, 5, 7, 8, 19, 22, 27, 31, 35, 44, 47, 48, 58, 66, 74, 75, 81, 88 ], [ 1, 2, 3, 5, 7, 8, 19, 22, 31, 33, 35, 41, 44, 51, 53, 60, 71, 72, 74, 95 ], [ 1, 2, 3, 5, 7, 8, 27, 31, 35, 39, 46, 51, 54, 59, 65, 74, 76, 80, 82, 96 ], [ 1, 2, 3, 5, 7, 8, 30, 31, 35, 39, 41, 46, 54, 57, 65, 66, 69, 74, 87, 90 ], [ 1, 2, 3, 5, 7, 8, 30, 31, 35, 39, 46, 54, 57, 65, 68, 74, 86, 88, 90, 95 ], [ 1, 2, 3, 5, 7, 8, 30, 31, 35, 39, 46, 54, 57, 65, 74, 79, 90, 91, 93, 96 ] ]; # Working on Small Group [96, 21]... # NO SOLUTION at level 4 with normal subgroup 2 and quotient [ 48, 5 ]. DS96[21] := [ ]; # Working on Small Group [96, 22]... # NO SOLUTION at level 4 with normal subgroup 2 and quotient [ 48, 5 ]. DS96[22] := [ ]; # Working on Small Group [96, 23]... # [96,23] has [48,6] image (so NO DS) DS96[23] := [ ]; # Working on Small Group [96, 24]... # NO SOLUTION at level 4 with normal subgroup 2 and quotient [ 48, 6 ]. DS96[24] := [ ]; # Working on Small Group [96, 25]... # [96,25] has [48,7] image (so NO DS) DS96[25] := [ ]; # Working on Small Group [96, 26]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[26] := [ ]; # Working on Small Group [96, 27]... # NO SOLUTION at level 4 with normal subgroup 2 and quotient [ 48, 5 ]. DS96[27] := [ ]; # Working on Small Group [96, 28]... # [96,28] has [48,6] and [48,7] images (so NO DS) DS96[28] := [ ]; # Working on Small Group [96, 29]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[29] := [ ]; # Working on Small Group [96, 30]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[30] := [ ]; # Working on Small Group [96, 31]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[31] := [ ]; # Working on Small Group [96, 32]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[32] := [ ]; # Working on Small Group [96, 33]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. # NO: [32,19] image DS96[33] := [ ]; # Working on Small Group [96, 34]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. # NO: [32,19] image DS96[34] := [ ]; # Working on Small Group [96, 35]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. # NO: [32,19] image DS96[35] := [ ]; # Working on Small Group [96, 36]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[36] := [ ]; # Working on Small Group [96, 37]... # [96,37] has [48,9] image (so NO DS) DS96[37] := [ ]; # Working on Small Group [96, 38]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[38] := [ ]; # Working on Small Group [96, 39]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[39] := [ ]; # Working on Small Group [96, 40]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[40] := [ ]; # Working on Small Group [96, 41]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 16 difference sets: DS96[41] := [ [ 1, 2, 3, 4, 7, 10, 12, 16, 24, 26, 33, 38, 39, 44, 57, 59, 81, 93, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 12, 22, 24, 26, 38, 43, 54, 60, 70, 71, 73, 76, 87, 95 ], [ 1, 2, 3, 4, 7, 10, 14, 16, 23, 30, 44, 48, 51, 52, 54, 67, 71, 74, 81, 89 ], [ 1, 2, 3, 4, 7, 10, 14, 16, 30, 34, 44, 51, 52, 54, 62, 67, 74, 81, 82, 94 ], [ 1, 2, 3, 4, 7, 10, 14, 16, 30, 41, 44, 51, 52, 54, 67, 69, 74, 81, 86, 95 ], [ 1, 2, 3, 4, 7, 10, 14, 16, 30, 44, 45, 47, 51, 52, 54, 67, 72, 73, 74, 81 ], [ 1, 2, 3, 4, 7, 10, 14, 16, 30, 44, 51, 52, 54, 55, 67, 74, 80, 81, 91, 96 ], [ 1, 2, 3, 4, 7, 10, 14, 16, 30, 44, 51, 52, 54, 66, 67, 68, 74, 81, 87, 88 ], [ 1, 2, 3, 4, 7, 10, 14, 22, 43, 45, 48, 52, 55, 68, 69, 70, 74, 82, 83, 92 ], [ 1, 2, 3, 4, 7, 10, 14, 22, 43, 52, 61, 62, 70, 71, 73, 74, 79, 86, 87, 96 ], [ 1, 2, 3, 4, 10, 12, 14, 33, 45, 48, 52, 55, 57, 68, 69, 74, 81, 82, 83, 92 ], [ 1, 2, 3, 4, 10, 12, 14, 33, 52, 57, 61, 62, 71, 73, 74, 79, 81, 86, 87, 96 ], [ 1, 2, 3, 4, 10, 12, 19, 22, 24, 26, 33, 38, 40, 57, 67, 79, 81, 82, 83, 91 ], [ 1, 2, 3, 4, 10, 14, 19, 21, 44, 45, 46, 48, 52, 55, 68, 69, 74, 82, 83, 92 ], [ 1, 2, 3, 4, 10, 14, 19, 21, 44, 46, 52, 61, 62, 71, 73, 74, 79, 86, 87, 96 ], [ 1, 2, 3, 4, 10, 14, 19, 22, 27, 39, 40, 52, 57, 58, 66, 68, 74, 76, 87, 88 ] ]; # Working on Small Group [96, 42]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[42] := [ ]; # Working on Small Group [96, 43]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[43] := [ ]; # Working on Small Group [96, 44]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[44] := [ ]; # Working on Small Group [96, 45]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[45] := [ ]; # Working on Small Group [96, 46]... # [96,46] has [48,23] image (so NO DS) DS96[46] := [ ]; # Working on Small Group [96, 47]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[47] := [ ]; # Working on Small Group [96, 48]... # [96,48] has [48,23] image (so NO DS) DS96[48] := [ ]; # Working on Small Group [96, 49]... # Both BruteForceSieve (early May 2006) and Omar say 'NO'. DS96[49] := [ ]; # Working on Small Group [96, 50]... # Both BruteForceSieve (early May 2006) and Omar say 'NO'. DS96[50] := [ ]; # Working on Small Group [96, 51]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 8 difference sets: DS96[51] := [ [ 1, 2, 3, 4, 5, 8, 16, 18, 19, 26, 32, 43, 58, 63, 73, 76, 86, 89, 92, 94 ], [ 1, 2, 3, 4, 5, 8, 16, 18, 19, 26, 43, 58, 62, 63, 73, 76, 81, 86, 89, 92 ], [ 1, 2, 3, 4, 5, 16, 18, 25, 32, 37, 53, 58, 63, 64, 86, 88, 91, 94, 95, 96 ], [ 1, 2, 3, 4, 5, 16, 18, 25, 37, 58, 62, 63, 64, 80, 81, 86, 88, 90, 91, 95 ], [ 1, 2, 3, 4, 6, 8, 12, 13, 19, 25, 29, 30, 39, 60, 66, 76, 81, 83, 84, 91 ], [ 1, 2, 3, 4, 6, 8, 12, 13, 19, 29, 39, 54, 60, 66, 74, 75, 76, 79, 90, 93 ], [ 1, 2, 3, 4, 6, 8, 12, 13, 19, 29, 54, 60, 69, 74, 75, 76, 79, 88, 90, 93 ], [ 1, 2, 3, 4, 6, 10, 13, 19, 30, 32, 58, 61, 62, 69, 75, 77, 79, 82, 88, 96 ] ]; # Working on Small Group [96, 52]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 4 difference sets: DS96[52] := [ [ 1, 2, 3, 4, 5, 8, 16, 17, 18, 29, 43, 51, 52, 55, 61, 62, 66, 71, 88, 89 ], [ 1, 2, 3, 4, 5, 8, 16, 19, 32, 43, 46, 49, 55, 58, 63, 70, 73, 86, 92, 94 ], [ 1, 2, 3, 4, 8, 10, 17, 18, 19, 27, 41, 45, 48, 64, 65, 74, 83, 89, 91, 94 ], [ 1, 2, 3, 4, 8, 10, 18, 19, 27, 35, 41, 43, 45, 48, 58, 71, 82, 87, 90, 96 ] ]; # Working on Small Group [96, 53]... # Both BruteForceSieve (early May 2006) and Omar say 'NO'. DS96[53] := [ ]; # Working on Small Group [96, 54]... # Omar has only 8; these 12 were generated by BruteForceSieve in early May 2006. # There are 12 difference sets: DS96[54] := [ [ 1, 2, 3, 4, 5, 8, 16, 18, 24, 29, 30, 32, 55, 58, 66, 79, 82, 83, 88, 94 ], [ 1, 2, 3, 4, 5, 8, 16, 18, 24, 30, 55, 56, 58, 60, 62, 66, 79, 81, 83, 88 ], [ 1, 2, 3, 4, 5, 8, 16, 32, 37, 38, 46, 50, 55, 65, 66, 68, 82, 83, 93, 95 ], [ 1, 2, 3, 4, 5, 11, 14, 21, 22, 43, 45, 50, 51, 58, 65, 72, 74, 75, 83, 86 ], [ 1, 2, 3, 4, 5, 16, 18, 25, 32, 50, 53, 58, 63, 64, 66, 67, 68, 77, 88, 94 ], [ 1, 2, 3, 4, 5, 21, 22, 34, 35, 40, 51, 63, 70, 73, 76, 78, 81, 82, 89, 90 ], [ 1, 2, 3, 4, 6, 11, 14, 21, 23, 42, 45, 50, 51, 58, 65, 71, 74, 75, 83, 86 ], [ 1, 2, 3, 4, 6, 12, 19, 26, 39, 51, 53, 56, 57, 59, 60, 61, 65, 77, 84, 95 ], [ 1, 2, 3, 4, 6, 12, 24, 28, 29, 38, 47, 50, 55, 56, 57, 60, 69, 80, 81, 88 ], [ 1, 2, 3, 4, 6, 12, 24, 29, 38, 39, 47, 50, 55, 58, 60, 66, 80, 82, 83, 94 ], [ 1, 2, 3, 4, 8, 10, 15, 18, 19, 21, 27, 42, 43, 45, 58, 65, 82, 87, 90, 96 ], [ 1, 2, 3, 4, 8, 10, 15, 19, 27, 43, 46, 48, 58, 65, 71, 73, 82, 87, 90, 96 ] ]; # Working on Small Group [96, 55]... # [96,55] has [48,23] image (so NO DS) DS96[55] := [ ]; # Working on Small Group [96, 56]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[56] := [ ]; # Working on Small Group [96, 57]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[57] := [ ]; # Working on Small Group [96, 58]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[58] := [ ]; # Working on Small Group [96, 59]... # [96,59] has [48,23] image (so NO DS) DS96[59] := [ ]; # Working on Small Group [96, 60]... # [96,60] has [48,23] image (so NO DS) DS96[60] := [ ]; # Working on Small Group [96, 61]... # [96,61] has [32,18] image (so NO DS) image DS96[61] := [ ]; # Working on Small Group [96, 62]... # [96,62] has [32,19] image (so NO DS) image DS96[62] := [ ]; # Working on Small Group [96, 63]... # Both BruteForceSieve (early May 2006) and Omar both say 'NO'. DS96[63] := [ ]; #################### # Chain length 5 # THIS IS A PARTIAL LIST, FROM THE WORK OF GOLEMAC, ET. AL. #################### DS96[64] := [ [ 1, 2, 3, 4, 5, 8, 24, 27, 28, 31, 32, 39, 43, 58, 60, 71, 73, 75, 90, 93 ], [ 1, 2, 3, 4, 5, 8, 13, 16, 17, 33, 44, 45, 54, 60, 61, 63, 65, 66, 83, 94 ] ]; # Working on Small Group [96, 65]... # Ruled out by BruteForceSieve, early May 2006 DS96[65] := [ ]; # Working on Small Group [96, 66]... # Ruled out by BruteForceSieve, early May 2006 -- also has [48,29] image (so no DS) DS96[66] := [ ]; # Working on Small Group [96, 67]... # Ruled out by BruteForceSieve, early May 2006 DS96[67] := [ ]; #################### # Chain length 5 # Working on Small Group [96, 68]... # There are 2 difference sets: # [96,68] has at least one difference set, says Anka Golemac DS96[68] := [ [ 1, 2, 3, 4, 5, 8, 13, 29, 32, 37, 38, 40, 43, 46, 55, 61, 68, 69, 83, 94 ], [ 1, 2, 3, 4, 5, 8, 29, 32, 35, 40, 43, 46, 55, 61, 64, 65, 69, 83, 87, 94 ] ]; #################### # Working on Small Group [96, 69]... # Ruled out by BruteForceSieve, early May 2006 # (I think this search only took 75 minutes.) DS96[69] := [ ]; #################### # Chain length 5 # THIS IS A PARTIAL LIST, FROM THE WORK OF GOLEMAC, ET. AL. # (Omar has six.) #################### DS96[70] := [ [ 1, 2, 3, 4, 5, 8, 11, 12, 18, 34, 40, 43, 49, 55, 78, 79, 80, 83, 89, 90 ], [ 1, 2, 3, 4, 5, 8, 11, 12, 18, 24, 34, 40, 43, 56, 76, 81, 82, 89, 90, 93 ], [ 1, 2, 3, 4, 5, 8, 11, 12, 18, 24, 34, 40, 43, 55, 77, 80, 83, 89, 91, 92 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 18, 31, 38, 40, 43, 58, 61, 66, 80, 81, 88, 89 ], [ 1, 2, 3, 4, 5, 8, 11, 18, 24, 31, 40, 43, 52, 58, 61, 77, 80, 81, 89, 93 ], [ 1, 2, 3, 4, 5, 8, 13, 18, 31, 37, 38, 40, 43, 56, 59, 62, 68, 81, 82, 89 ], # The following two found by "magic" and verified to be inequivalent from the others # g:= SmallGroup(96,70); e:=Elements(g);; CL := ConvolutionTable_f( g, e, x->x^-1);; # v:=96; for d1 in DS do # int:=Size(Set(MultisetToList(Convolution_AsMultiset(CL, d1,d1),v))); # if int=2 then Print(d1,"\n"); fi;; od; [ 1, 2, 3, 4, 5, 8, 11, 18, 31, 35, 40, 43, 58, 61, 65, 80, 81, 85, 89, 95 ], [ 1, 2, 3, 4, 5, 8, 11, 18, 31, 40, 43, 49, 58, 61, 76, 80, 81, 89, 90, 96 ] ]; #################### # Chain length 5 # THIS IS A PARTIAL LIST, FROM THE WORK OF GOLEMAC, ET. AL. #################### DS96[71] := [ [ 1, 2, 3, 4, 5, 9, 18, 26, 28, 33, 40, 42, 60, 74, 81, 82, 89, 90, 91, 96 ], [ 1, 2, 3, 4, 5, 9, 13, 18, 26, 28, 33, 37, 38, 40, 42, 60, 68, 81, 82, 89 ] ]; #################### # Chain length 5 # THIS IS A PARTIAL LIST, FROM THE WORK OF GOLEMAC, ET. AL. #################### DS96[72] := [ [ 1, 2, 3, 4, 5, 8, 13, 30, 33, 37, 38, 39, 42, 46, 55, 59, 68, 71, 83, 94 ] ]; # Working on Small Group [96, 73]... # Ruled out by BruteForceSieve, early May 2006 DS96[73] := [ ]; # Working on Small Group [96, 74]... # Ruled out by BruteForceSieve, early May 2006 DS96[74] := [ ]; # Working on Small Group [96, 75]... # Omar lists 52; BruteForceSieve (early May 2006) gives 88. # There are 88 difference sets: DS96[75] := [ [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 23, 30, 46, 53, 56, 68, 74, 75, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 30, 45, 46, 53, 56, 69, 73, 74, 75, 86 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 30, 46, 47, 56, 69, 72, 74, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 30, 46, 48, 56, 68, 71, 74, 78, 87, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 19, 28, 32, 33, 36, 39, 60, 62, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 23, 28, 36, 46, 72, 74, 76, 78, 81, 88, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 28, 30, 36, 41, 46, 72, 73, 74, 75, 78, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 28, 36, 41, 46, 47, 53, 58, 72, 74, 75, 86 ], [ 1, 2, 3, 4, 7, 8, 12, 23, 30, 36, 37, 39, 47, 48, 49, 53, 56, 70, 73, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 23, 36, 37, 43, 47, 48, 49, 56, 58, 67, 73, 78, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 30, 36, 37, 39, 41, 49, 53, 56, 68, 69, 70, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 30, 36, 37, 39, 45, 49, 53, 56, 70, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 30, 36, 37, 39, 49, 53, 56, 66, 70, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 36, 37, 41, 43, 49, 56, 58, 67, 68, 69, 78, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 36, 37, 43, 45, 49, 56, 58, 67, 71, 72, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 36, 37, 43, 49, 56, 58, 66, 67, 78, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 32, 46, 54, 56, 57, 66, 74, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 33, 46, 53, 56, 58, 66, 74, 75, 88, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 54, 56, 60, 68, 74, 76, 81, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 55, 56, 61, 68, 74, 77, 82, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 56, 61, 66, 74, 80, 82, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 56, 62, 66, 74, 79, 83, 88, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 56, 62, 68, 74, 83, 87, 89, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 32, 41, 46, 47, 51, 56, 57, 72, 74, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 32, 46, 48, 51, 56, 57, 66, 71, 74, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 46, 47, 51, 56, 60, 69, 72, 74, 81, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 46, 48, 51, 56, 60, 68, 71, 74, 81, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 32, 41, 45, 46, 54, 56, 57, 73, 74, 76, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 33, 41, 45, 46, 53, 56, 58, 73, 74, 75, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 33, 41, 46, 47, 56, 58, 72, 74, 78, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 33, 46, 48, 56, 58, 66, 71, 74, 78, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 34, 41, 46, 47, 56, 59, 72, 74, 79, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 34, 46, 47, 56, 59, 69, 72, 74, 86, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 34, 46, 48, 56, 59, 66, 71, 74, 79, 88, 91 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 34, 46, 48, 56, 59, 68, 71, 74, 87, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 41, 45, 46, 56, 61, 73, 74, 80, 82, 92, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 41, 45, 46, 56, 62, 73, 74, 79, 83, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 41, 46, 47, 56, 72, 74, 80, 84, 92, 94, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 45, 46, 54, 56, 60, 69, 73, 74, 76, 81, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 45, 46, 55, 56, 61, 69, 73, 74, 77, 82, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 45, 46, 56, 62, 69, 73, 74, 83, 86, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 46, 47, 55, 56, 69, 72, 74, 77, 84, 86, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 46, 48, 55, 56, 68, 71, 74, 77, 84, 87, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 46, 48, 56, 66, 71, 74, 80, 84, 88, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 28, 36, 39, 47, 48, 62, 73, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 30, 36, 39, 47, 48, 49, 54, 56, 60, 73, 85, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 27, 28, 36, 39, 53, 54, 62, 74, 77, 78, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 36, 39, 41, 62, 68, 69, 74, 77, 85, 88, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 30, 34, 36, 39, 49, 54, 56, 60, 61, 62, 84, 85, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 30, 36, 39, 41, 49, 54, 56, 60, 68, 69, 85, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 30, 36, 39, 49, 54, 55, 56, 60, 79, 80, 85, 90, 93 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 27, 28, 32, 36, 46, 51, 66, 68, 74, 81, 89 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 27, 28, 36, 46, 60, 66, 71, 74, 76, 81, 88 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 36, 46, 49, 55, 56, 72, 83, 84, 88, 95, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 27, 28, 30, 36, 41, 46, 60, 66, 71, 73, 74, 75 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 30, 33, 36, 45, 46, 69, 73, 74, 78, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 32, 36, 46, 47, 54, 58, 69, 74, 87, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 32, 36, 46, 48, 51, 54, 57, 68, 74, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 33, 36, 45, 46, 47, 53, 58, 69, 74, 86, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 33, 36, 45, 46, 48, 51, 53, 57, 68, 74, 86 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 36, 46, 48, 54, 57, 60, 71, 74, 76, 87, 88 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 34, 36, 41, 46, 49, 56, 66, 71, 73, 77, 82, 93 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 36, 45, 46, 48, 49, 56, 59, 61, 68, 80, 86, 91 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 36, 46, 47, 49, 56, 62, 69, 79, 87, 89, 92, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 24, 25, 32, 33, 35, 44, 60, 80, 82, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 24, 32, 33, 37, 52, 60, 62, 63, 70, 79, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 12, 19, 24, 32, 33, 40, 52, 60, 63, 64, 80, 84, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 25, 35, 46, 66, 69, 75, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 23, 35, 37, 40, 47, 48, 50, 52, 53, 70, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 35, 37, 40, 41, 50, 52, 53, 68, 69, 70, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 35, 37, 40, 45, 50, 52, 53, 70, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 35, 37, 40, 50, 52, 53, 66, 70, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 25, 35, 44, 47, 48, 73, 80, 82, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 37, 47, 48, 52, 62, 63, 70, 73, 79, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 27, 35, 44, 47, 48, 50, 52, 57, 60, 73, 85, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 25, 30, 35, 44, 57, 58, 80, 81, 82, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 25, 35, 44, 45, 71, 72, 80, 82, 84, 85, 89, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 30, 37, 52, 57, 58, 62, 63, 70, 79, 81, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 37, 45, 52, 62, 63, 70, 71, 72, 79, 82, 89, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 27, 34, 35, 44, 50, 52, 57, 60, 61, 62, 84, 85, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 27, 35, 44, 45, 50, 52, 57, 60, 71, 72, 85, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 27, 35, 44, 50, 52, 57, 59, 60, 82, 83, 85, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 19, 23, 24, 40, 47, 48, 52, 63, 64, 73, 80, 84, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 19, 24, 27, 40, 52, 53, 54, 63, 64, 78, 80, 84, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 19, 24, 40, 41, 52, 63, 64, 68, 69, 80, 84, 88, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 27, 30, 35, 45, 46, 60, 68, 73, 76, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 46, 47, 51, 54, 58, 72, 86, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 33, 35, 41, 46, 48, 53, 57, 71, 87, 90 ] ]; # Working on Small Group [96, 76]... # [96,76] has [48,36] image (so NO DS) DS96[76] := [ ]; # Working on Small Group [96, 77]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 40 difference sets: DS96[77] := [ [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 59, 61, 69, 71, 92, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 59, 61, 71, 80, 87, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 61, 66, 80, 83, 88, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 61, 69, 77, 83, 86, 89, 93 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 45, 46, 47, 69, 82, 92, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 45, 46, 47, 80, 82, 87, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 46, 47, 66, 72, 80, 88, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 46, 47, 69, 72, 77, 86, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 45, 46, 62, 73, 79, 82, 92, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 46, 48, 59, 71, 79, 84, 92, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 46, 48, 77, 79, 83, 84, 86, 89 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 46, 62, 72, 73, 77, 79, 86, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 45, 46, 55, 62, 68, 73, 82, 87, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 46, 48, 55, 59, 68, 71, 84, 87, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 46, 48, 55, 66, 68, 83, 84, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 46, 55, 62, 66, 68, 72, 73, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 16, 23, 36, 43, 47, 48, 50, 51, 58, 60, 73, 78, 85 ], [ 1, 2, 3, 4, 7, 8, 9, 16, 34, 36, 43, 50, 51, 58, 60, 61, 62, 78, 84, 85 ], [ 1, 2, 3, 4, 7, 8, 9, 16, 36, 43, 45, 50, 51, 58, 60, 71, 72, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 8, 9, 16, 36, 43, 50, 51, 58, 59, 60, 78, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 23, 36, 46, 50, 55, 66, 71, 83, 84, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 34, 36, 41, 46, 50, 72, 73, 77, 82, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 36, 45, 46, 47, 50, 62, 69, 79, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 36, 46, 48, 50, 59, 61, 68, 80, 87, 89, 91 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 24, 32, 33, 43, 52, 55, 60, 63, 65, 83, 84, 92 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 25, 32, 33, 43, 50, 60, 63, 65, 77, 80, 83, 84 ], [ 1, 2, 3, 4, 7, 9, 12, 19, 25, 32, 33, 40, 50, 60, 61, 63, 64, 80, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 12, 19, 32, 33, 35, 40, 50, 52, 55, 60, 61, 82, 85, 91 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 35, 46, 47, 50, 52, 53, 72, 81, 86, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 23, 24, 25, 35, 37, 40, 47, 48, 70, 73, 75, 78, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 24, 25, 35, 37, 40, 41, 68, 69, 70, 75, 78, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 24, 25, 35, 37, 40, 45, 70, 71, 72, 75, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 26, 36, 43, 47, 48, 53, 58, 60, 73, 76, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 33, 43, 47, 48, 52, 53, 63, 65, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 43, 47, 48, 52, 55, 63, 65, 73, 83, 84, 92 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 26, 34, 36, 43, 53, 58, 60, 61, 62, 76, 84, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 26, 36, 43, 45, 53, 58, 60, 71, 72, 76, 85, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 33, 34, 43, 52, 53, 61, 62, 63, 65, 81, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 33, 43, 45, 52, 53, 63, 65, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 43, 45, 52, 55, 63, 65, 71, 72, 83, 84, 89, 92 ] ]; # Working on Small Group [96, 78]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 8) # There are 10 difference sets: DS96[78] := [ [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 44, 54, 75, 81, 82, 85, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 54, 55, 75, 81, 83, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 37, 40, 43, 53, 63, 75, 81, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 39, 41, 44, 49, 56, 57, 68, 69, 76, 78, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 39, 44, 45, 49, 56, 57, 71, 72, 76, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 39, 44, 49, 56, 57, 66, 76, 78, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 25, 37, 40, 41, 43, 49, 56, 58, 63, 68, 69, 76, 78, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 26, 27, 46, 49, 56, 58, 60, 68, 72, 75, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 30, 32, 45, 46, 48, 49, 54, 56, 86, 88, 90 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 33, 41, 46, 47, 49, 51, 53, 56, 81, 87, 89 ] ]; # Working on Small Group [96, 79]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 14) # There are 24 difference sets: DS96[79] := [ [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 25, 46, 49, 55, 62, 66, 82, 88, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 34, 46, 48, 49, 68, 71, 80, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 41, 45, 46, 49, 61, 73, 77, 83, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 46, 47, 49, 59, 69, 72, 79, 84, 86, 92 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 35, 44, 47, 48, 50, 52, 54, 73, 75, 81, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 34, 35, 44, 50, 52, 54, 61, 62, 75, 81, 84, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 45, 50, 52, 54, 71, 72, 75, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 50, 52, 54, 59, 75, 81, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 62, 66, 69, 82, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 36, 46, 49, 52, 61, 66, 68, 83, 89, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 41, 46, 48, 50, 52, 71, 79, 87, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 36, 41, 46, 47, 49, 52, 72, 80, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 45, 46, 50, 52, 55, 61, 68, 73, 83, 92, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 46, 47, 50, 52, 59, 72, 77, 80, 84, 86, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 36, 45, 46, 49, 52, 55, 62, 69, 73, 82, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 36, 46, 48, 49, 52, 59, 71, 77, 79, 84, 87, 88 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 37, 54, 57, 59, 62, 67, 70, 90, 91, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 44, 54, 57, 59, 64, 67, 80, 84, 90, 91 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 27, 29, 33, 46, 66, 74, 75, 81, 88, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 46, 50, 51, 53, 56, 58, 60, 72, 86, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 27, 33, 46, 47, 50, 56, 66, 69, 75, 81, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 29, 30, 32, 41, 45, 46, 73, 74, 76, 78, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 29, 46, 47, 51, 53, 58, 60, 69, 72, 74, 86 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 30, 32, 45, 46, 48, 50, 56, 68, 76, 78, 95 ] ]; # Working on Small Group [96, 80]... # [96,80] has [48,36] image (so NO DS) DS96[80] := [ ]; # Working on Small Group [96, 81]... # [96,81] has [48,36] image (so NO DS) DS96[81] := [ ]; # Working on Small Group [96, 82]... # [96,82] has [48,36] image (so NO DS) DS96[82] := [ ]; # Working on Small Group [96, 83]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 18 difference sets: DS96[83] := [ [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 29, 46, 50, 59, 61, 66, 80, 88, 89, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 29, 46, 50, 59, 61, 69, 86, 89, 92, 93 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 34, 46, 47, 50, 66, 72, 80, 82, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 34, 46, 47, 50, 69, 72, 82, 86, 92, 93 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 41, 45, 46, 50, 62, 73, 77, 79, 94, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 41, 46, 48, 50, 71, 77, 79, 83, 84, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 45, 46, 50, 55, 62, 68, 73, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 46, 48, 50, 55, 68, 71, 83, 84, 87, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 40, 53, 58, 64, 70, 82, 90, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 37, 53, 58, 59, 61, 67, 70, 90, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 40, 51, 53, 58, 63, 65, 70, 82, 91, 93 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 40, 41, 57, 64, 68, 69, 70, 74, 76, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 40, 45, 57, 64, 70, 71, 72, 74, 76, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 40, 57, 64, 66, 70, 74, 76, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 41, 57, 63, 65, 68, 69, 70, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 29, 46, 59, 61, 66, 74, 88, 89, 92, 93 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 29, 41, 45, 46, 55, 62, 73, 74, 91, 94, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 29, 46, 48, 68, 71, 74, 77, 79, 83, 84, 87 ] ]; # Working on Small Group [96, 84]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 72 difference sets: DS96[84] := [ [ 1, 2, 3, 4, 7, 9, 12, 13, 23, 39, 47, 48, 52, 54, 65, 70, 73, 74, 75, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 41, 52, 54, 65, 68, 69, 70, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 45, 52, 54, 65, 70, 71, 72, 74, 75, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 52, 54, 65, 66, 70, 74, 75, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 25, 35, 46, 66, 69, 75, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 25, 46, 50, 63, 69, 78, 81, 87, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 36, 46, 49, 52, 54, 66, 68, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 41, 46, 48, 71, 75, 78, 81, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 51, 58, 68, 71, 73, 78, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 41, 46, 48, 52, 53, 63, 66, 71, 75, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 25, 41, 46, 48, 50, 63, 66, 71, 78, 81, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 36, 41, 46, 47, 49, 52, 54, 72, 81, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 24, 25, 35, 37, 40, 41, 68, 69, 70, 75, 78, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 24, 25, 35, 37, 40, 45, 70, 71, 72, 75, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 24, 25, 35, 37, 40, 66, 70, 75, 78, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 25, 40, 41, 50, 63, 65, 68, 69, 70, 78, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 25, 40, 45, 50, 63, 65, 70, 71, 72, 78, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 25, 40, 50, 63, 65, 66, 70, 78, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 46, 52, 61, 68, 74, 77, 83, 87, 89, 93 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 34, 41, 46, 47, 52, 72, 74, 80, 91, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 45, 46, 52, 55, 62, 69, 73, 74, 82, 86, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 46, 48, 52, 59, 66, 71, 74, 79, 84, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 35, 46, 57, 60, 69, 72, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 33, 35, 46, 53, 57, 66, 69, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 35, 46, 62, 66, 69, 79, 82, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 33, 46, 52, 57, 63, 69, 78, 87, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 46, 50, 55, 63, 69, 72, 82, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 32, 36, 46, 49, 52, 58, 66, 68, 76, 78, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 62, 66, 69, 82, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 27, 30, 35, 46, 47, 60, 72, 76, 86, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 33, 35, 46, 47, 53, 66, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 41, 45, 46, 48, 54, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 45, 46, 51, 54, 58, 68, 73, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 45, 46, 61, 68, 73, 77, 80, 83, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 46, 47, 55, 59, 72, 84, 86, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 27, 32, 45, 46, 51, 52, 58, 63, 68, 73, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 30, 46, 47, 52, 54, 60, 63, 72, 76, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 46, 50, 63, 66, 68, 71, 73, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 41, 45, 46, 48, 50, 61, 63, 80, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 46, 47, 50, 59, 62, 63, 77, 79, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 27, 33, 36, 45, 46, 49, 52, 57, 69, 73, 75, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 27, 33, 36, 46, 48, 49, 52, 57, 71, 75, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 30, 36, 45, 46, 49, 51, 52, 53, 60, 69, 73, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 30, 36, 46, 48, 49, 51, 52, 53, 60, 71, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 32, 36, 41, 46, 47, 49, 52, 58, 72, 76, 78, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 41, 46, 48, 50, 52, 71, 79, 87, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 45, 46, 50, 52, 55, 61, 68, 73, 83, 92, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 46, 47, 50, 52, 59, 72, 77, 80, 84, 86, 88 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 54, 57, 61, 65, 70, 77, 80, 90, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 51, 55, 58, 61, 78, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 51, 53, 58, 61, 63, 64, 80, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 40, 43, 51, 58, 65, 78, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 37, 40, 57, 59, 62, 70, 77, 78, 90, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 39, 58, 59, 61, 70, 77, 78, 90, 93 ], [ 1, 2, 3, 4, 7, 12, 24, 29, 35, 40, 41, 43, 52, 53, 65, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 24, 29, 35, 40, 43, 45, 52, 53, 65, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 24, 29, 35, 40, 43, 52, 53, 65, 66, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 46, 50, 51, 53, 56, 58, 60, 72, 86, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 27, 33, 46, 47, 50, 56, 66, 69, 75, 81, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 30, 32, 45, 46, 48, 50, 56, 68, 76, 78, 95 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 25, 29, 32, 40, 47, 48, 54, 63, 64, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 27, 29, 32, 35, 40, 47, 48, 52, 73, 81, 85, 90 ], [ 1, 2, 3, 4, 7, 19, 24, 25, 29, 32, 40, 41, 54, 63, 64, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 19, 24, 25, 29, 32, 40, 54, 55, 63, 64, 79, 80, 81, 90, 93 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 32, 35, 40, 41, 52, 68, 69, 81, 85, 88, 90 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 32, 35, 40, 52, 55, 79, 80, 81, 85, 90, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 25, 29, 46, 62, 63, 69, 79, 87, 89, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 25, 36, 46, 56, 72, 79, 83, 84, 88, 92, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 29, 45, 46, 59, 61, 63, 68, 73, 77, 80, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 29, 46, 47, 55, 63, 72, 83, 84, 88, 92, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 36, 45, 46, 48, 56, 59, 61, 68, 77, 86, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 36, 46, 47, 55, 56, 62, 69, 87, 89, 94, 96 ] ]; # Working on Small Group [96, 85]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 72) # There are 136 difference sets: DS96[85] := [ [ 1, 2, 3, 4, 7, 8, 12, 19, 29, 32, 33, 35, 40, 60, 61, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 29, 35, 46, 47, 54, 57, 72, 74, 76, 86, 88 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 24, 32, 40, 47, 48, 56, 58, 63, 64, 73, 78, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 29, 35, 40, 47, 48, 61, 73, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 24, 32, 34, 40, 56, 58, 61, 62, 63, 64, 78, 84, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 24, 32, 40, 41, 56, 58, 63, 64, 68, 69, 78, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 24, 32, 40, 55, 56, 58, 63, 64, 78, 79, 80, 90, 93 ], [ 1, 2, 3, 4, 7, 8, 19, 27, 29, 35, 40, 53, 54, 61, 74, 77, 78, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 35, 40, 41, 61, 68, 69, 74, 77, 85, 88, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 46, 56, 61, 63, 69, 77, 82, 87, 89, 93 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 29, 30, 32, 35, 46, 66, 69, 74, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 34, 46, 47, 56, 59, 63, 72, 80, 88, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 41, 46, 48, 56, 63, 66, 71, 79, 84, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 45, 46, 55, 56, 62, 63, 68, 73, 83, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 27, 29, 33, 35, 45, 46, 51, 68, 73, 74, 81, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 29, 35, 41, 46, 48, 53, 58, 60, 71, 74, 75, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 23, 26, 39, 47, 48, 50, 51, 65, 70, 73, 78, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 23, 39, 47, 48, 52, 54, 65, 70, 73, 74, 75, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 26, 39, 41, 50, 51, 65, 68, 69, 70, 78, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 26, 39, 45, 50, 51, 65, 70, 71, 72, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 26, 39, 50, 51, 65, 66, 70, 78, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 41, 52, 54, 65, 68, 69, 70, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 45, 52, 54, 65, 70, 71, 72, 74, 75, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 52, 54, 65, 66, 70, 74, 75, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 26, 36, 46, 53, 58, 72, 75, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 26, 36, 46, 66, 68, 76, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 46, 52, 53, 63, 69, 75, 81, 87, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 46, 52, 54, 63, 68, 76, 81, 86, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 26, 46, 49, 51, 53, 58, 63, 72, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 26, 46, 49, 63, 68, 78, 81, 86, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 23, 35, 37, 40, 47, 48, 50, 52, 53, 70, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 35, 37, 40, 41, 50, 52, 53, 68, 69, 70, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 35, 37, 40, 45, 50, 52, 53, 70, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 35, 37, 40, 50, 52, 53, 66, 70, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 26, 46, 50, 61, 68, 72, 77, 80, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 26, 46, 50, 61, 68, 80, 83, 87, 89, 91 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 46, 52, 61, 68, 74, 77, 83, 87, 89, 93 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 34, 41, 46, 47, 50, 72, 77, 93, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 34, 41, 46, 47, 50, 83, 87, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 45, 46, 48, 50, 55, 82, 84, 86, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 45, 46, 50, 62, 69, 73, 79, 82, 86, 92 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 46, 48, 50, 55, 59, 66, 71, 84, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 46, 50, 59, 62, 66, 69, 71, 73, 79, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 34, 41, 46, 47, 52, 72, 74, 80, 91, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 45, 46, 52, 55, 62, 69, 73, 74, 82, 86, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 46, 48, 52, 59, 66, 71, 74, 79, 84, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 55, 61, 69, 72, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 27, 30, 36, 45, 46, 60, 69, 73, 75, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 27, 32, 36, 46, 47, 51, 69, 81, 87, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 30, 33, 36, 45, 46, 48, 68, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 32, 36, 41, 46, 47, 54, 58, 72, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 33, 36, 46, 48, 51, 53, 57, 71, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 36, 41, 46, 54, 57, 60, 66, 71, 73, 76 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 27, 32, 46, 47, 51, 52, 58, 63, 72, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 27, 33, 46, 48, 51, 52, 57, 63, 71, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 30, 45, 46, 52, 53, 60, 63, 69, 73, 75, 87 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 30, 45, 46, 52, 54, 60, 63, 68, 73, 76, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 32, 41, 46, 47, 52, 58, 63, 66, 72, 78, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 33, 41, 46, 48, 52, 57, 63, 66, 71, 78, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 27, 30, 45, 46, 49, 51, 60, 63, 69, 73, 87 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 27, 32, 46, 47, 49, 63, 69, 75, 81, 89, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 30, 33, 45, 46, 48, 49, 63, 66, 68, 76, 78 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 32, 41, 46, 47, 49, 54, 58, 63, 66, 72, 76 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 33, 46, 48, 49, 53, 57, 63, 71, 75, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 41, 46, 49, 54, 57, 60, 63, 71, 73, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 46, 47, 50, 52, 66, 79, 83, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 41, 45, 46, 48, 50, 52, 80, 82, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 46, 50, 52, 59, 62, 68, 71, 73, 77, 87, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 54, 57, 65, 70, 83, 90, 91, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 43, 51, 54, 58, 65, 67, 79, 92, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 44, 54, 57, 64, 67, 79, 90, 92, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 51, 55, 58, 61, 78, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 53, 61, 63, 64, 75, 80, 81, 83, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 37, 40, 57, 70, 78, 79, 83, 90, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 37, 44, 54, 57, 67, 76, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 39, 54, 57, 70, 76, 77, 83, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 39, 57, 70, 78, 80, 83, 85, 90, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 36, 37, 39, 54, 58, 70, 76, 77, 82, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 36, 37, 39, 58, 70, 78, 80, 82, 90, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 36, 37, 43, 53, 58, 67, 75, 80, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 40, 51, 53, 58, 63, 65, 70, 82, 91, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 39, 54, 58, 59, 61, 70, 76, 80, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 39, 58, 59, 61, 70, 77, 78, 90, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 39, 44, 59, 61, 64, 76, 77, 78, 81, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 40, 44, 53, 59, 61, 63, 75, 77, 80, 81, 85 ], [ 1, 2, 3, 4, 7, 12, 13, 24, 26, 29, 41, 43, 53, 65, 67, 68, 69, 76, 81, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 24, 26, 29, 43, 45, 53, 65, 67, 71, 72, 76, 81, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 24, 26, 29, 43, 53, 65, 66, 67, 76, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 41, 58, 65, 68, 69, 70, 74, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 45, 58, 65, 70, 71, 72, 74, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 58, 65, 66, 70, 74, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 41, 44, 53, 64, 67, 68, 69, 74, 76, 81, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 44, 45, 53, 64, 67, 71, 72, 74, 76, 81, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 44, 53, 64, 66, 67, 74, 76, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 41, 57, 63, 65, 68, 69, 70, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 45, 57, 63, 65, 70, 71, 72, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 57, 63, 65, 66, 70, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 37, 41, 43, 49, 54, 67, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 37, 43, 45, 49, 54, 67, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 37, 43, 49, 54, 66, 67, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 12, 26, 28, 35, 37, 41, 44, 50, 53, 67, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 26, 28, 35, 37, 44, 45, 50, 53, 67, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 26, 28, 35, 37, 44, 50, 53, 66, 67, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 12, 26, 28, 35, 39, 41, 50, 51, 58, 68, 69, 70, 78, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 26, 28, 35, 39, 45, 50, 51, 58, 70, 71, 72, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 26, 28, 35, 39, 50, 51, 58, 66, 70, 78, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 26, 29, 36, 37, 39, 41, 50, 51, 57, 68, 69, 70, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 26, 29, 36, 37, 39, 45, 50, 51, 57, 70, 71, 72, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 26, 29, 36, 37, 39, 50, 51, 57, 66, 70, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 28, 35, 37, 40, 41, 52, 53, 58, 68, 69, 70, 74, 76, 88 ], [ 1, 2, 3, 4, 7, 12, 28, 35, 37, 40, 45, 52, 53, 58, 70, 71, 72, 74, 76, 89 ], [ 1, 2, 3, 4, 7, 12, 28, 35, 37, 40, 52, 53, 58, 66, 70, 74, 76, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 28, 35, 39, 41, 52, 54, 58, 68, 69, 70, 74, 75, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 28, 35, 39, 45, 52, 54, 58, 70, 71, 72, 74, 75, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 28, 35, 39, 52, 54, 58, 66, 70, 74, 75, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 29, 36, 37, 39, 41, 52, 54, 57, 68, 69, 70, 74, 75, 88 ], [ 1, 2, 3, 4, 7, 12, 29, 36, 37, 39, 45, 52, 54, 57, 70, 71, 72, 74, 75, 89 ], [ 1, 2, 3, 4, 7, 12, 29, 36, 37, 39, 52, 54, 57, 66, 70, 74, 75, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 27, 29, 32, 35, 40, 47, 48, 52, 73, 81, 85, 90 ], [ 1, 2, 3, 4, 7, 19, 23, 25, 32, 40, 47, 48, 49, 54, 56, 58, 63, 64, 73, 76 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 32, 35, 40, 41, 52, 68, 69, 81, 85, 88, 90 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 32, 35, 40, 52, 55, 79, 80, 81, 85, 90, 93 ], [ 1, 2, 3, 4, 7, 19, 25, 32, 40, 41, 49, 54, 56, 58, 63, 64, 68, 69, 76, 88 ], [ 1, 2, 3, 4, 7, 19, 25, 32, 40, 49, 54, 55, 56, 58, 63, 64, 76, 79, 80, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 28, 32, 36, 46, 52, 66, 68, 78, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 46, 49, 56, 59, 61, 63, 69, 72, 77, 80, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 26, 28, 32, 36, 46, 49, 54, 58, 68, 72, 86, 90 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 26, 28, 32, 36, 46, 49, 54, 66, 68, 76, 81, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 27, 28, 30, 33, 36, 45, 46, 51, 52, 69, 73, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 28, 36, 46, 48, 52, 53, 57, 60, 71, 75, 87, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 41, 45, 46, 48, 49, 55, 56, 63, 83, 84, 86, 92 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 46, 49, 56, 62, 63, 66, 68, 71, 73, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 27, 28, 30, 36, 45, 46, 48, 49, 60, 75, 88, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 27, 28, 36, 46, 48, 49, 51, 57, 60, 71, 87, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 30, 33, 36, 45, 46, 49, 53, 69, 73, 75, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 33, 36, 46, 49, 51, 53, 57, 69, 71, 73, 87 ] ]; # Working on Small Group [96, 86]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 34) # There are 48 difference sets: DS96[86] := [ [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 23, 36, 46, 50, 55, 66, 71, 83, 84, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 34, 36, 41, 46, 50, 72, 73, 77, 82, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 36, 45, 46, 47, 50, 62, 69, 79, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 36, 46, 48, 50, 59, 61, 68, 80, 87, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 41, 46, 56, 58, 72, 73, 74, 75, 78, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 27, 46, 56, 57, 60, 71, 74, 76, 87, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 30, 33, 45, 46, 47, 53, 56, 69, 74, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 32, 46, 48, 51, 54, 56, 66, 68, 74, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 51, 58, 68, 71, 73, 78, 87 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 32, 44, 47, 48, 52, 54, 63, 64, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 35, 44, 47, 48, 50, 52, 54, 73, 75, 81, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 32, 34, 44, 52, 54, 61, 62, 63, 64, 81, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 32, 44, 45, 52, 54, 63, 64, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 32, 44, 52, 54, 59, 63, 64, 81, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 34, 35, 44, 50, 52, 54, 61, 62, 75, 81, 84, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 45, 50, 52, 54, 71, 72, 75, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 50, 52, 54, 59, 75, 81, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 35, 46, 57, 60, 69, 72, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 33, 35, 46, 47, 53, 66, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 41, 45, 46, 48, 54, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 40, 58, 64, 70, 75, 77, 78, 79, 82 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 35, 44, 57, 61, 77, 78, 80, 83, 85, 90 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 44, 57, 61, 63, 64, 75, 78, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 36, 40, 53, 58, 70, 75, 77, 82, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 37, 40, 53, 55, 57, 70, 75, 82, 84, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 40, 44, 53, 55, 63, 75, 81, 83, 84, 85, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 40, 57, 63, 65, 70, 75, 78, 80, 82, 84, 96 ], [ 1, 2, 3, 4, 7, 12, 13, 29, 40, 41, 49, 51, 52, 53, 57, 64, 68, 69, 70, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 29, 40, 45, 49, 51, 52, 53, 57, 64, 70, 71, 72, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 29, 40, 49, 51, 52, 53, 57, 64, 66, 70, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 40, 41, 49, 51, 57, 68, 69, 70, 78, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 40, 45, 49, 51, 57, 70, 71, 72, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 40, 49, 51, 57, 66, 70, 78, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 16, 23, 28, 32, 35, 44, 47, 48, 51, 52, 54, 58, 73, 74, 85 ], [ 1, 2, 3, 4, 7, 16, 23, 28, 32, 44, 47, 48, 49, 52, 54, 58, 63, 64, 73, 76 ], [ 1, 2, 3, 4, 7, 16, 28, 32, 35, 44, 45, 51, 52, 54, 58, 71, 72, 74, 85, 89 ], [ 1, 2, 3, 4, 7, 16, 28, 32, 35, 44, 51, 52, 54, 58, 59, 74, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 16, 28, 32, 44, 45, 49, 52, 54, 58, 63, 64, 71, 72, 76, 89 ], [ 1, 2, 3, 4, 7, 16, 28, 32, 44, 49, 52, 54, 58, 59, 63, 64, 76, 82, 83, 94 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 25, 27, 29, 46, 58, 60, 63, 69, 76, 87, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 29, 35, 46, 52, 54, 58, 60, 66, 69, 76, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 46, 49, 55, 56, 63, 69, 72, 83, 84, 92, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 29, 30, 32, 41, 46, 48, 51, 54, 63, 66, 71 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 29, 33, 46, 47, 53, 63, 72, 81, 88, 90, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 27, 29, 30, 32, 35, 41, 46, 48, 51, 52, 71, 87 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 29, 33, 35, 46, 47, 52, 72, 78, 81, 86, 88, 90 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 41, 45, 46, 48, 49, 56, 59, 61, 63, 77, 80, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 46, 47, 49, 56, 62, 63, 79, 87, 88, 89, 94, 96 ] ]; # Working on Small Group [96, 87]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 16 difference sets: DS96[87] := [ [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 54, 57, 65, 70, 83, 90, 91, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 37, 40, 57, 70, 78, 79, 83, 90, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 40, 43, 51, 58, 65, 78, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 36, 37, 39, 58, 70, 78, 80, 82, 90, 91 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 41, 58, 65, 68, 69, 70, 74, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 45, 58, 65, 70, 71, 72, 74, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 58, 65, 66, 70, 74, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 41, 57, 63, 65, 68, 69, 70, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 45, 57, 63, 65, 70, 71, 72, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 57, 63, 65, 66, 70, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 36, 41, 44, 54, 56, 57, 67, 68, 69, 75, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 36, 44, 45, 54, 56, 57, 67, 71, 72, 75, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 36, 44, 54, 56, 57, 66, 67, 75, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 29, 35, 40, 41, 43, 52, 53, 65, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 24, 29, 35, 40, 43, 45, 52, 53, 65, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 24, 29, 35, 40, 43, 52, 53, 65, 66, 81, 86, 87, 90, 95 ] ]; # Working on Small Group [96, 88]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 26) # There are 48 difference sets: DS96[88] := [ [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 46, 49, 59, 62, 68, 87, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 46, 49, 62, 68, 72, 77, 82, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 46, 49, 68, 77, 80, 82, 84, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 56, 61, 71, 74, 77, 80, 87, 88, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 34, 45, 46, 48, 49, 79, 86, 88, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 34, 45, 46, 49, 69, 73, 79, 83, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 34, 46, 48, 49, 66, 71, 79, 83, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 41, 46, 47, 49, 59, 62, 72, 91, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 41, 46, 47, 49, 59, 80, 84, 87, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 41, 46, 47, 49, 72, 77, 80, 82, 84, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 45, 46, 49, 55, 61, 69, 73, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 46, 48, 49, 55, 61, 66, 71, 88, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 46, 49, 55, 61, 66, 69, 71, 73, 83, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 34, 45, 46, 47, 56, 69, 74, 83, 91, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 41, 46, 56, 59, 62, 72, 73, 74, 79, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 46, 48, 55, 56, 66, 68, 74, 82, 84, 89, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 53, 58, 61, 76, 80, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 51, 53, 58, 61, 63, 64, 80, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 37, 40, 53, 57, 59, 62, 70, 75, 79, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 39, 55, 58, 62, 70, 78, 90, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 39, 58, 70, 78, 79, 83, 84, 90, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 43, 53, 58, 61, 67, 75, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 39, 44, 55, 62, 64, 76, 78, 81, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 40, 51, 53, 58, 62, 63, 65, 70, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 25, 29, 32, 40, 47, 48, 54, 63, 64, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 29, 35, 40, 47, 48, 52, 55, 61, 73, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 19, 24, 25, 29, 32, 40, 41, 54, 63, 64, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 19, 24, 25, 29, 32, 40, 54, 55, 63, 64, 79, 80, 81, 90, 93 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 35, 40, 52, 53, 54, 55, 61, 78, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 19, 24, 29, 35, 40, 41, 52, 55, 61, 68, 69, 85, 88, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 25, 29, 46, 62, 63, 69, 79, 87, 89, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 29, 33, 35, 46, 52, 66, 69, 78, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 29, 36, 46, 49, 61, 66, 71, 83, 88, 92, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 26, 27, 28, 36, 46, 49, 51, 57, 60, 66, 68, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 26, 28, 30, 33, 36, 46, 49, 53, 66, 68, 75, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 26, 28, 33, 36, 46, 49, 51, 53, 57, 68, 72, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 29, 45, 46, 59, 61, 63, 68, 73, 77, 80, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 29, 46, 47, 55, 63, 72, 83, 84, 88, 92, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 27, 29, 30, 32, 35, 45, 46, 51, 52, 68, 73, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 29, 35, 46, 47, 52, 54, 58, 60, 72, 76, 86, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 29, 36, 41, 46, 49, 55, 62, 72, 73, 82, 91, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 29, 36, 46, 48, 49, 59, 68, 77, 79, 84, 87, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 27, 28, 30, 36, 41, 46, 47, 49, 60, 66, 75, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 27, 28, 36, 41, 46, 47, 49, 51, 57, 60, 72, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 30, 33, 36, 41, 46, 47, 49, 53, 72, 75, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 32, 36, 45, 46, 49, 54, 69, 73, 76, 81, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 32, 36, 46, 48, 49, 54, 71, 76, 81, 87, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 32, 36, 46, 49, 54, 58, 69, 71, 73, 87, 90 ] ]; # Working on Small Group [96, 89]... # [96,89] has [48,36] image (so NO DS) DS96[89] := [ ]; # Working on Small Group [96, 90]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 24 difference sets: DS96[90] := [ [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 35, 44, 47, 48, 50, 52, 54, 73, 75, 81, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 34, 35, 44, 50, 52, 54, 61, 62, 75, 81, 84, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 45, 50, 52, 54, 71, 72, 75, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 50, 52, 54, 59, 75, 81, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 43, 51, 54, 55, 58, 61, 65, 67, 83, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 44, 59, 61, 63, 64, 77, 78, 80, 81, 90 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 55, 61, 75, 78, 81, 83, 85, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 51, 53, 58, 61, 63, 64, 80, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 43, 53, 58, 61, 67, 75, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 24, 26, 29, 46, 55, 61, 71, 83, 87, 88, 96 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 41, 46, 62, 72, 73, 77, 82, 86, 93 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 46, 48, 59, 66, 68, 80, 84, 89, 91 ], [ 1, 2, 3, 4, 7, 16, 23, 28, 44, 47, 48, 49, 52, 61, 63, 64, 73, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 16, 28, 30, 44, 49, 52, 57, 58, 61, 63, 64, 80, 81, 83, 92 ], [ 1, 2, 3, 4, 7, 16, 28, 44, 45, 49, 52, 61, 63, 64, 71, 72, 80, 83, 89, 92 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 25, 29, 32, 40, 47, 48, 54, 63, 64, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 19, 23, 25, 35, 40, 47, 48, 56, 61, 73, 74, 77, 80, 83, 85 ], [ 1, 2, 3, 4, 7, 19, 24, 25, 29, 32, 40, 41, 54, 63, 64, 68, 69, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 19, 24, 25, 29, 32, 40, 54, 55, 63, 64, 79, 80, 81, 90, 93 ], [ 1, 2, 3, 4, 7, 19, 25, 27, 35, 40, 53, 54, 56, 61, 74, 77, 78, 80, 83, 85 ], [ 1, 2, 3, 4, 7, 19, 25, 35, 40, 41, 56, 61, 68, 69, 74, 77, 80, 83, 85, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 29, 36, 46, 49, 61, 66, 71, 83, 88, 92, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 29, 36, 41, 46, 49, 55, 62, 72, 73, 82, 91, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 29, 36, 46, 48, 49, 59, 68, 77, 79, 84, 87, 89 ] ]; # Working on Small Group [96, 91]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 4) # There are 8 difference sets: DS96[91] := [ [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 46, 50, 55, 63, 69, 72, 82, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 46, 50, 63, 66, 68, 71, 73, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 41, 45, 46, 48, 50, 61, 63, 80, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 46, 47, 50, 59, 62, 63, 77, 79, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 40, 44, 57, 59, 64, 77, 78, 80, 84, 90 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 27, 35, 46, 51, 56, 58, 60, 69, 72, 74, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 30, 32, 35, 41, 45, 46, 48, 54, 56, 74, 76, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 33, 35, 46, 47, 53, 56, 66, 74, 75, 81, 88, 89 ] ]; # Working on Small Group [96, 92]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 40 difference sets: DS96[92] := [ [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 46, 52, 55, 61, 63, 69, 72, 91, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 34, 46, 47, 52, 63, 77, 79, 83, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 41, 45, 46, 48, 52, 63, 80, 82, 84, 86, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 46, 52, 59, 62, 63, 66, 68, 71, 73, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 40, 53, 58, 64, 70, 82, 90, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 53, 55, 58, 76, 82, 84, 85, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 53, 55, 57, 63, 64, 83, 84, 90, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 37, 40, 53, 58, 70, 76, 82, 93, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 36, 40, 53, 58, 70, 75, 77, 82, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 40, 51, 53, 58, 63, 65, 70, 82, 91, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 37, 40, 53, 55, 57, 70, 75, 82, 84, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 40, 44, 55, 57, 61, 64, 78, 83, 90, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 40, 53, 55, 57, 63, 65, 70, 82, 84, 90, 91 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 40, 41, 57, 64, 68, 69, 70, 74, 76, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 40, 45, 57, 64, 70, 71, 72, 74, 76, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 40, 57, 64, 66, 70, 74, 76, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 41, 57, 63, 65, 68, 69, 70, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 45, 57, 63, 65, 70, 71, 72, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 57, 63, 65, 66, 70, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 35, 37, 40, 41, 50, 57, 68, 69, 70, 78, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 35, 37, 40, 45, 50, 57, 70, 71, 72, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 35, 37, 40, 50, 57, 66, 70, 78, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 40, 41, 49, 51, 57, 68, 69, 70, 78, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 40, 45, 49, 51, 57, 70, 71, 72, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 25, 29, 36, 40, 49, 51, 57, 66, 70, 78, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 29, 35, 40, 47, 48, 52, 73, 80, 82, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 19, 23, 25, 27, 28, 40, 47, 48, 58, 60, 63, 64, 73, 74, 76 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 35, 40, 52, 53, 54, 78, 80, 82, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 19, 24, 29, 35, 40, 41, 52, 68, 69, 80, 82, 84, 85, 88, 91 ], [ 1, 2, 3, 4, 7, 19, 25, 27, 28, 40, 41, 58, 60, 63, 64, 68, 69, 74, 76, 88 ], [ 1, 2, 3, 4, 7, 19, 25, 27, 28, 40, 55, 58, 60, 63, 64, 74, 76, 79, 80, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 29, 35, 46, 52, 54, 58, 60, 66, 69, 76, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 28, 46, 55, 63, 69, 74, 82, 84, 87, 89, 91 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 30, 32, 35, 46, 54, 56, 69, 72, 74, 76, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 27, 29, 30, 32, 35, 41, 46, 48, 51, 52, 71, 87 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 29, 33, 35, 46, 47, 52, 72, 78, 81, 86, 88, 90 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 27, 35, 41, 45, 46, 48, 51, 56, 58, 60, 74, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 28, 41, 46, 48, 61, 63, 66, 71, 74, 80, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 28, 46, 47, 59, 62, 63, 72, 74, 77, 79, 88, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 33, 35, 46, 53, 56, 68, 71, 73, 74, 75, 81, 87 ] ]; # [96,93] has [48,36] image (so NO DS) DS96[93] := [ ]; # Working on Small Group [96, 94]... # From Omar's work; verified by BruteForceSieve in early May 2006. # There are 84 difference sets: DS96[94] := [ [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 23, 28, 30, 46, 49, 71, 78, 87, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 28, 30, 46, 48, 49, 66, 68, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 28, 41, 46, 49, 51, 71, 73, 78, 81, 87 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 28, 46, 47, 49, 51, 66, 69, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 28, 46, 49, 54, 68, 71, 73, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 23, 28, 44, 47, 48, 49, 51, 64, 67, 73, 78, 81 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 28, 41, 44, 49, 51, 64, 67, 68, 69, 78, 81, 88 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 28, 44, 45, 49, 51, 64, 67, 71, 72, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 28, 44, 49, 51, 64, 66, 67, 78, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 16, 24, 32, 33, 44, 56, 60, 63, 64, 83, 84, 91, 93 ], [ 1, 2, 3, 4, 7, 8, 12, 16, 28, 32, 33, 36, 37, 44, 59, 60, 74, 84, 92, 93 ], [ 1, 2, 3, 4, 7, 8, 12, 19, 28, 32, 33, 36, 39, 60, 74, 80, 83, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 23, 28, 40, 47, 48, 49, 51, 53, 58, 60, 65, 73 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 28, 34, 40, 49, 51, 53, 58, 60, 61, 62, 65, 84 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 28, 40, 41, 49, 51, 53, 58, 60, 65, 68, 69, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 28, 40, 49, 51, 53, 55, 58, 60, 65, 79, 80, 93 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 27, 28, 30, 46, 49, 60, 72, 86, 88, 90 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 30, 46, 49, 53, 60, 66, 69, 72, 76 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 32, 46, 49, 54, 58, 72, 75, 86, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 33, 46, 49, 53, 58, 71, 75, 87, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 46, 49, 55, 71, 77, 84, 87, 88, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 46, 49, 61, 71, 80, 82, 87, 88, 92 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 46, 49, 62, 72, 79, 82, 86, 88, 92 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 28, 30, 45, 46, 48, 49, 60, 68, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 28, 33, 46, 47, 49, 57, 86, 88, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 28, 41, 46, 49, 51, 60, 72, 73, 81, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 28, 45, 46, 47, 49, 51, 60, 69, 81, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 32, 41, 45, 46, 48, 49, 51, 58, 78, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 32, 41, 46, 49, 54, 57, 72, 73, 76, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 32, 45, 46, 47, 49, 54, 57, 69, 76, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 32, 45, 46, 48, 49, 54, 58, 68, 75, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 33, 41, 46, 49, 53, 57, 71, 73, 76, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 33, 46, 47, 49, 53, 57, 66, 69, 76, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 33, 46, 48, 49, 53, 58, 66, 68, 75, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 34, 41, 46, 49, 59, 72, 73, 86, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 34, 45, 46, 47, 49, 59, 69, 93, 95, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 34, 45, 46, 48, 49, 68, 77, 93, 94, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 41, 46, 49, 61, 71, 73, 80, 83, 87, 91 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 41, 46, 49, 62, 72, 73, 79, 83, 86, 91 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 45, 46, 47, 49, 62, 69, 79, 83, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 46, 47, 49, 55, 59, 66, 69, 84, 89, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 46, 48, 49, 55, 66, 68, 77, 84, 89, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 46, 48, 49, 61, 66, 68, 80, 82, 89, 92 ], [ 1, 2, 3, 4, 7, 8, 16, 23, 24, 44, 47, 48, 56, 58, 60, 63, 64, 73, 75, 78 ], [ 1, 2, 3, 4, 7, 8, 16, 23, 24, 44, 47, 48, 56, 63, 64, 73, 83, 84, 91, 93 ], [ 1, 2, 3, 4, 7, 8, 16, 24, 30, 44, 56, 57, 58, 63, 64, 81, 83, 84, 91, 93 ], [ 1, 2, 3, 4, 7, 8, 16, 24, 44, 45, 56, 58, 60, 63, 64, 71, 72, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 8, 16, 24, 44, 45, 56, 63, 64, 71, 72, 83, 84, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 8, 16, 24, 44, 56, 58, 59, 60, 63, 64, 75, 78, 82, 83, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 28, 36, 39, 47, 48, 73, 74, 80, 83, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 28, 39, 47, 48, 50, 51, 54, 58, 60, 63, 65, 73 ], [ 1, 2, 3, 4, 7, 8, 19, 27, 28, 36, 39, 53, 54, 74, 78, 80, 83, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 34, 39, 50, 51, 54, 58, 60, 61, 62, 63, 65, 84 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 36, 39, 41, 68, 69, 74, 80, 83, 84, 85, 88, 91 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 39, 41, 50, 51, 54, 58, 60, 63, 65, 68, 69, 88 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 39, 50, 51, 54, 55, 58, 60, 63, 65, 79, 80, 93 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 25, 32, 33, 36, 43, 60, 62, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 48, 54, 57, 68, 76, 86, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 51, 58, 68, 71, 73, 78, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 57, 68, 72, 73, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 25, 46, 49, 55, 62, 71, 87, 88, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 25, 46, 49, 55, 66, 69, 72, 82, 84, 92 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 25, 46, 49, 55, 69, 71, 83, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 34, 46, 48, 49, 66, 68, 80, 82, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 34, 46, 49, 66, 68, 72, 73, 82, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 34, 46, 49, 68, 71, 73, 83, 91, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 41, 45, 46, 48, 49, 61, 77, 80, 87, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 41, 46, 48, 49, 59, 61, 80, 86, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 41, 46, 49, 59, 61, 72, 73, 86, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 45, 46, 47, 49, 62, 77, 79, 87, 88, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 45, 46, 47, 49, 69, 77, 79, 83, 84, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 46, 47, 49, 59, 62, 79, 86, 88, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 25, 33, 43, 47, 48, 50, 63, 65, 73, 75, 78, 81 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 30, 36, 43, 57, 58, 62, 74, 77, 81, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 33, 43, 45, 50, 63, 65, 71, 72, 75, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 33, 35, 46, 51, 71, 81, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 35, 46, 51, 58, 60, 69, 71, 87 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 35, 46, 57, 60, 69, 72, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 32, 35, 41, 46, 48, 54, 66, 76, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 32, 35, 41, 46, 66, 72, 73, 78, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 33, 35, 46, 47, 53, 66, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 41, 45, 46, 48, 54, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 33, 35, 45, 46, 47, 53, 75, 81, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 45, 46, 47, 53, 58, 60, 69, 75, 87 ] ]; # Working on Small Group [96, 95]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar gets 60 ) # There are 96 difference sets: DS96[95] := [ [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 23, 46, 56, 57, 72, 74, 76, 78, 86, 88 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 29, 30, 46, 47, 50, 66, 69, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 29, 46, 47, 50, 57, 69, 72, 76, 78, 86 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 30, 46, 47, 56, 69, 72, 74, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 23, 29, 43, 47, 48, 50, 51, 65, 67, 73, 78, 81 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 29, 41, 43, 50, 51, 65, 67, 68, 69, 78, 81, 88 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 29, 43, 45, 50, 51, 65, 67, 71, 72, 78, 81, 89 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 29, 43, 50, 51, 65, 66, 67, 78, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 19, 24, 32, 33, 37, 56, 60, 61, 63, 67, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 8, 12, 19, 29, 32, 33, 40, 49, 60, 61, 63, 64, 92, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 23, 29, 32, 47, 48, 50, 51, 54, 67, 73, 81, 85 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 23, 32, 47, 48, 54, 56, 58, 67, 73, 74, 75, 85 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 29, 32, 34, 50, 51, 54, 61, 62, 67, 81, 84, 85 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 29, 32, 41, 50, 51, 54, 67, 68, 69, 81, 85, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 29, 32, 50, 51, 54, 55, 67, 79, 80, 81, 85, 93 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 32, 34, 54, 56, 58, 61, 62, 67, 74, 75, 84, 85 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 32, 41, 54, 56, 58, 67, 68, 69, 74, 75, 85, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 32, 54, 55, 56, 58, 67, 74, 75, 79, 80, 85, 93 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 29, 30, 32, 46, 50, 54, 66, 88, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 29, 32, 46, 50, 54, 57, 72, 76, 86, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 32, 46, 54, 56, 57, 66, 74, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 56, 61, 71, 74, 77, 80, 87, 88, 94 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 29, 45, 46, 48, 50, 51, 60, 68, 81, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 29, 46, 48, 50, 58, 60, 68, 71, 75, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 41, 46, 56, 58, 60, 71, 73, 74, 75, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 46, 48, 51, 56, 60, 68, 71, 74, 81, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 33, 41, 45, 46, 50, 51, 53, 73, 81, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 29, 33, 41, 46, 50, 53, 58, 71, 73, 75, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 30, 32, 46, 47, 54, 56, 66, 69, 74, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 33, 41, 45, 46, 53, 56, 58, 73, 74, 75, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 33, 45, 46, 48, 51, 53, 56, 68, 74, 81, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 34, 45, 46, 47, 56, 69, 74, 83, 91, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 41, 46, 56, 59, 62, 72, 73, 74, 79, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 46, 48, 55, 56, 66, 68, 74, 82, 84, 89, 92 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 24, 37, 47, 48, 56, 61, 63, 67, 73, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 29, 32, 35, 47, 48, 54, 65, 67, 73, 74, 75, 81 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 29, 40, 47, 48, 49, 61, 63, 64, 73, 92, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 32, 35, 40, 47, 48, 50, 56, 58, 73, 75, 78, 85 ], [ 1, 2, 3, 4, 7, 8, 19, 24, 27, 37, 53, 54, 56, 61, 63, 67, 78, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 8, 19, 24, 37, 41, 56, 61, 63, 67, 68, 69, 80, 83, 88, 92 ], [ 1, 2, 3, 4, 7, 8, 19, 27, 29, 40, 49, 53, 54, 61, 63, 64, 78, 92, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 32, 34, 35, 54, 61, 62, 65, 67, 74, 75, 81, 84 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 32, 35, 41, 54, 65, 67, 68, 69, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 32, 35, 54, 55, 65, 67, 74, 75, 79, 80, 81, 93 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 40, 41, 49, 61, 63, 64, 68, 69, 88, 92, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 32, 34, 35, 40, 50, 56, 58, 61, 62, 75, 78, 84, 85 ], [ 1, 2, 3, 4, 7, 8, 19, 32, 35, 40, 41, 50, 56, 58, 68, 69, 75, 78, 85, 88 ], [ 1, 2, 3, 4, 7, 8, 19, 32, 35, 40, 50, 55, 56, 58, 75, 78, 79, 80, 85, 93 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 24, 26, 36, 46, 58, 68, 72, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 23, 36, 46, 49, 52, 54, 66, 68, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 26, 36, 41, 46, 47, 72, 76, 78, 81, 86 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 26, 36, 46, 47, 51, 53, 69, 72, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 46, 52, 61, 68, 72, 74, 91, 93, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 45, 46, 48, 52, 74, 79, 82, 84, 86, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 46, 52, 55, 59, 62, 66, 69, 71, 73, 74, 92 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 26, 32, 35, 47, 48, 58, 65, 70, 73, 74, 75, 78 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 35, 44, 47, 48, 50, 52, 54, 73, 75, 81, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 26, 32, 34, 35, 58, 61, 62, 65, 70, 74, 75, 78, 84 ], [ 1, 2, 3, 4, 7, 9, 16, 26, 32, 35, 45, 58, 65, 70, 71, 72, 74, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 26, 32, 35, 58, 59, 65, 70, 74, 75, 78, 82, 83, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 34, 35, 44, 50, 52, 54, 61, 62, 75, 81, 84, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 45, 50, 52, 54, 71, 72, 75, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 50, 52, 54, 59, 75, 81, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 26, 27, 32, 36, 46, 58, 75, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 26, 35, 46, 55, 61, 74, 83, 86, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 26, 35, 46, 61, 68, 72, 74, 80, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 61, 68, 83, 89, 91, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 27, 36, 46, 51, 57, 60, 69, 71, 73, 87 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 30, 33, 36, 45, 46, 48, 53, 75, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 30, 36, 46, 48, 54, 60, 66, 68, 71, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 32, 36, 41, 46, 47, 54, 66, 76, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 26, 33, 36, 41, 45, 46, 57, 73, 76, 78, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 34, 35, 41, 46, 47, 74, 77, 83, 89, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 34, 35, 46, 47, 66, 69, 72, 74, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 35, 41, 45, 46, 62, 73, 74, 82, 87, 91, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 35, 45, 46, 48, 55, 66, 74, 82, 84, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 35, 46, 48, 59, 68, 71, 74, 77, 80, 84, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 26, 35, 46, 59, 62, 69, 71, 73, 74, 79, 86, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 27, 33, 36, 46, 48, 49, 52, 57, 71, 75, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 30, 36, 45, 46, 49, 51, 52, 53, 60, 69, 73, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 32, 36, 41, 46, 47, 49, 52, 58, 72, 76, 78, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 41, 46, 47, 50, 52, 72, 77, 80, 87, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 45, 46, 50, 52, 55, 62, 66, 69, 73, 82, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 46, 48, 50, 52, 59, 71, 79, 84, 86, 88, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 37, 54, 55, 57, 61, 67, 70, 90, 92, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 54, 57, 61, 65, 70, 77, 80, 90, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 53, 61, 65, 67, 81, 83, 90, 91, 93 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 29, 30, 32, 46, 66, 74, 76, 78, 88, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 26, 28, 46, 61, 68, 74, 77, 80, 87, 89, 94 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 27, 29, 33, 41, 45, 46, 73, 74, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 29, 46, 48, 51, 53, 58, 60, 68, 71, 74, 87 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 28, 45, 46, 59, 62, 69, 73, 74, 79, 86, 96 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 28, 46, 48, 55, 66, 71, 74, 82, 84, 88, 92 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 26, 35, 47, 48, 55, 56, 61, 65, 67, 73, 83, 92 ], [ 1, 2, 3, 4, 7, 19, 24, 26, 27, 35, 53, 54, 55, 56, 61, 65, 67, 78, 83, 92 ], [ 1, 2, 3, 4, 7, 19, 24, 26, 35, 41, 55, 56, 61, 65, 67, 68, 69, 83, 88, 92 ] ]; # Working on Small Group [96, 96]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar has 120) # There are 120 difference sets: DS96[96] := [ [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 59, 61, 69, 71, 92, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 59, 61, 71, 80, 87, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 45, 46, 47, 69, 82, 92, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 45, 46, 47, 80, 82, 87, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 46, 48, 77, 79, 83, 84, 86, 89 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 46, 62, 72, 73, 77, 79, 86, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 46, 48, 55, 66, 68, 83, 84, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 46, 55, 62, 66, 68, 72, 73, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 23, 36, 46, 50, 59, 61, 66, 71, 80, 88, 91 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 34, 36, 45, 46, 47, 50, 69, 77, 82, 86, 93 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 36, 41, 46, 50, 62, 72, 73, 79, 92, 94, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 21, 22, 36, 46, 48, 50, 55, 68, 83, 84, 87, 89, 96 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 28, 30, 45, 46, 47, 49, 69, 78, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 30, 46, 47, 56, 69, 72, 74, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 41, 46, 56, 58, 72, 73, 74, 75, 78, 86 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 21, 22, 46, 51, 54, 56, 58, 66, 68, 72, 73, 74 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 28, 30, 36, 45, 46, 47, 51, 54, 66, 74, 88 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 28, 30, 36, 45, 46, 47, 69, 74, 75, 78, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 27, 46, 56, 57, 60, 71, 74, 76, 87, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 28, 32, 46, 49, 54, 57, 71, 76, 87, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 32, 46, 54, 56, 57, 66, 74, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 23, 46, 53, 56, 57, 60, 69, 71, 74, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 28, 46, 48, 49, 51, 60, 66, 68, 81, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 30, 33, 45, 46, 47, 56, 74, 76, 87, 88 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 27, 46, 48, 51, 56, 60, 68, 71, 74, 81, 87 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 28, 33, 41, 46, 49, 53, 58, 72, 73, 75, 86 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 30, 33, 45, 46, 47, 53, 56, 69, 74, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 32, 41, 46, 48, 56, 74, 75, 78, 81, 86, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 32, 46, 48, 51, 54, 56, 66, 68, 74, 81, 89 ], [ 1, 2, 3, 4, 7, 8, 13, 21, 22, 33, 41, 45, 46, 53, 56, 58, 73, 74, 75, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 29, 36, 46, 55, 59, 66, 71, 84, 88, 91 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 29, 36, 46, 59, 61, 80, 87, 88, 89, 91 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 29, 36, 46, 59, 69, 71, 77, 79, 84, 86 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 28, 32, 36, 46, 51, 54, 57, 66, 71, 74, 88 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 28, 32, 36, 46, 57, 69, 71, 74, 75, 78, 86 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 34, 36, 41, 46, 72, 73, 92, 93, 94, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 34, 36, 46, 47, 69, 72, 77, 82, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 34, 36, 46, 68, 72, 73, 80, 87, 94, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 36, 41, 45, 46, 62, 73, 79, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 36, 41, 46, 48, 61, 83, 89, 92, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 36, 45, 46, 47, 55, 62, 66, 82, 88, 91 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 36, 45, 46, 47, 62, 69, 77, 79, 82, 86 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 36, 46, 48, 55, 66, 68, 71, 83, 84, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 29, 36, 46, 48, 61, 68, 80, 83, 87, 89, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 27, 28, 33, 36, 46, 58, 68, 72, 73, 74, 76, 87 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 27, 28, 36, 46, 48, 60, 68, 74, 76, 81, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 33, 36, 41, 46, 53, 58, 72, 73, 74, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 36, 41, 46, 48, 53, 60, 74, 81, 89, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 35, 50, 52, 60, 61, 65, 70, 77, 80, 83 ], [ 1, 2, 3, 4, 7, 9, 12, 19, 24, 25, 32, 33, 35, 40, 60, 61, 80, 82, 85, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 19, 32, 33, 35, 40, 50, 52, 60, 80, 84, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 57, 68, 72, 73, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 46, 52, 53, 57, 63, 68, 72, 73, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 46, 52, 62, 69, 71, 74, 92, 93, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 34, 41, 46, 48, 52, 74, 77, 79, 82, 86, 89 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 45, 46, 47, 52, 74, 80, 83, 84, 87, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 46, 52, 55, 59, 61, 66, 68, 72, 73, 74, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 26, 32, 36, 47, 48, 58, 64, 70, 73, 76, 78 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 32, 44, 47, 48, 52, 54, 63, 64, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 35, 47, 48, 50, 52, 61, 65, 70, 73, 77, 80, 83 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 26, 32, 34, 36, 58, 61, 62, 64, 70, 76, 78, 84 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 26, 32, 36, 45, 58, 64, 70, 71, 72, 76, 78, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 26, 32, 36, 58, 59, 64, 70, 76, 78, 82, 83, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 32, 34, 44, 52, 54, 61, 62, 63, 64, 81, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 32, 44, 45, 52, 54, 63, 64, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 32, 44, 52, 54, 59, 63, 64, 81, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 30, 35, 50, 52, 57, 58, 61, 65, 70, 77, 80, 81, 83 ], [ 1, 2, 3, 4, 7, 9, 16, 35, 45, 50, 52, 61, 65, 70, 71, 72, 77, 80, 83, 89 ], [ 1, 2, 3, 4, 7, 9, 19, 23, 24, 25, 27, 35, 40, 47, 48, 60, 73, 75, 81, 85 ], [ 1, 2, 3, 4, 7, 9, 19, 23, 24, 25, 35, 40, 47, 48, 61, 73, 80, 82, 85, 96 ], [ 1, 2, 3, 4, 7, 9, 19, 24, 25, 27, 35, 40, 41, 60, 68, 69, 75, 81, 85, 88 ], [ 1, 2, 3, 4, 7, 9, 19, 24, 25, 27, 35, 40, 53, 54, 61, 78, 80, 82, 85, 96 ], [ 1, 2, 3, 4, 7, 9, 19, 24, 25, 27, 35, 40, 55, 60, 75, 79, 80, 81, 85, 93 ], [ 1, 2, 3, 4, 7, 9, 19, 24, 25, 35, 40, 41, 61, 68, 69, 80, 82, 85, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 35, 46, 51, 58, 60, 69, 71, 87 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 35, 46, 62, 69, 71, 79, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 46, 51, 52, 54, 58, 60, 63, 66, 69, 71 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 46, 52, 62, 63, 66, 69, 71, 91, 93, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 36, 46, 62, 69, 71, 74, 79, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 36, 46, 49, 52, 61, 66, 68, 83, 89, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 32, 35, 41, 46, 48, 54, 66, 76, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 33, 35, 45, 46, 47, 53, 75, 81, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 34, 35, 41, 46, 48, 66, 82, 89, 93, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 45, 46, 47, 55, 77, 83, 84, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 46, 59, 61, 68, 72, 73, 80, 86, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 27, 30, 32, 41, 46, 48, 52, 63, 76, 87, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 33, 45, 46, 47, 52, 63, 75, 78, 81, 86, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 34, 41, 46, 48, 52, 63, 79, 82, 87, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 45, 46, 47, 52, 63, 77, 80, 83, 84, 86, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 46, 52, 55, 59, 61, 63, 68, 72, 73, 92, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 36, 41, 46, 48, 74, 77, 82, 89, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 36, 45, 46, 47, 55, 66, 74, 83, 84, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 36, 46, 59, 61, 68, 72, 73, 74, 80, 87, 91 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 36, 41, 46, 47, 49, 52, 72, 80, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 36, 45, 46, 49, 52, 55, 62, 69, 73, 82, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 36, 46, 48, 49, 52, 59, 71, 77, 79, 84, 87, 88 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 16, 31, 51, 54, 58, 59, 61, 70, 85, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 51, 54, 58, 59, 61, 65, 70, 80, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 35, 44, 59, 61, 75, 78, 80, 81, 85, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 37, 57, 61, 63, 70, 75, 78, 80, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 53, 57, 59, 61, 63, 64, 77, 80, 90 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 57, 63, 64, 75, 77, 78, 80, 83, 84 ], [ 1, 2, 3, 4, 7, 13, 16, 23, 24, 26, 29, 30, 32, 47, 48, 70, 73, 76, 78, 85 ], [ 1, 2, 3, 4, 7, 13, 16, 24, 26, 29, 30, 32, 45, 70, 71, 72, 76, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 13, 16, 24, 26, 29, 30, 32, 59, 70, 76, 78, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 24, 26, 29, 46, 59, 61, 68, 80, 87, 89, 96 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 45, 46, 62, 69, 73, 77, 79, 86, 94 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 46, 48, 55, 66, 71, 83, 84, 88, 91 ], [ 1, 2, 3, 4, 7, 16, 23, 28, 32, 37, 47, 48, 49, 52, 54, 63, 70, 73, 81, 90 ], [ 1, 2, 3, 4, 7, 16, 23, 28, 35, 44, 47, 48, 52, 61, 73, 74, 77, 80, 83, 85 ], [ 1, 2, 3, 4, 7, 16, 28, 30, 35, 44, 52, 57, 58, 61, 74, 77, 80, 81, 83, 85 ], [ 1, 2, 3, 4, 7, 16, 28, 32, 37, 45, 49, 52, 54, 63, 70, 71, 72, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 16, 28, 32, 37, 49, 52, 54, 59, 63, 70, 81, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 16, 28, 35, 44, 45, 52, 61, 71, 72, 74, 77, 80, 83, 85, 89 ], [ 1, 2, 3, 4, 7, 19, 23, 25, 28, 30, 32, 40, 47, 48, 51, 54, 63, 64, 73, 74 ], [ 1, 2, 3, 4, 7, 19, 23, 25, 28, 40, 47, 48, 55, 63, 64, 73, 74, 83, 84, 92 ], [ 1, 2, 3, 4, 7, 19, 25, 27, 28, 40, 53, 54, 55, 63, 64, 74, 78, 83, 84, 92 ], [ 1, 2, 3, 4, 7, 19, 25, 28, 30, 32, 40, 41, 51, 54, 63, 64, 68, 69, 74, 88 ], [ 1, 2, 3, 4, 7, 19, 25, 28, 30, 32, 40, 51, 54, 55, 63, 64, 74, 79, 80, 93 ], [ 1, 2, 3, 4, 7, 19, 25, 28, 40, 41, 55, 63, 64, 68, 69, 74, 83, 84, 88, 92 ] ]; # Working on Small Group [96, 97]... # From Omar's work; verified by BruteForceSieve in early May 2006. # (Omar found 16) # There are 16 difference sets: DS96[ 97 ] := [ [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 23, 24, 46, 62, 66, 79, 82, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 34, 46, 48, 68, 71, 77, 87, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 41, 45, 46, 61, 73, 80, 83, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 9, 13, 21, 22, 24, 46, 47, 55, 59, 69, 72, 84, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 12, 13, 19, 32, 33, 56, 60, 62, 67, 74, 79, 82, 85, 92 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 23, 47, 48, 56, 62, 67, 73, 74, 79, 82, 85, 92 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 27, 53, 54, 56, 62, 67, 74, 78, 79, 82, 85, 92 ], [ 1, 2, 3, 4, 7, 8, 13, 19, 41, 56, 62, 67, 68, 69, 74, 79, 82, 85, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 24, 32, 33, 37, 52, 60, 62, 63, 70, 79, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 35, 50, 52, 60, 62, 65, 70, 79, 82, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 33, 37, 47, 48, 52, 53, 57, 63, 70, 73, 75 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 37, 47, 48, 52, 62, 63, 70, 73, 79, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 30, 37, 52, 57, 58, 62, 63, 70, 79, 81, 82, 91 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 33, 37, 45, 52, 53, 57, 63, 70, 71, 72, 75, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 33, 37, 52, 53, 57, 59, 63, 70, 75, 82, 83, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 37, 45, 52, 62, 63, 70, 71, 72, 79, 82, 89, 91 ] ]; # Working on Small Group [96, 98]... # There are 24 difference sets: # (Omar found 8) DS96[ 98 ] := [ [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 19, 31, 53, 61, 67, 76, 77, 81, 83, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 43, 53, 58, 65, 67, 80, 90, 91, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 44, 54, 57, 64, 67, 79, 90, 92, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 37, 54, 55, 57, 61, 67, 70, 90, 92, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 57, 61, 76, 77, 78, 83, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 54, 57, 61, 65, 70, 77, 80, 90, 94 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 41, 43, 54, 65, 67, 68, 69, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 43, 45, 54, 65, 67, 71, 72, 74, 75, 81, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 25, 29, 43, 54, 65, 66, 67, 74, 75, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 41, 44, 53, 64, 67, 68, 69, 74, 76, 81, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 44, 45, 53, 64, 67, 71, 72, 74, 76, 81, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 44, 53, 64, 66, 67, 74, 76, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 13, 19, 23, 25, 32, 47, 48, 50, 51, 56, 58, 67, 73, 78, 85 ], [ 1, 2, 3, 4, 7, 13, 19, 25, 32, 41, 50, 51, 56, 58, 67, 68, 69, 78, 85, 88 ], [ 1, 2, 3, 4, 7, 13, 19, 25, 32, 50, 51, 55, 56, 58, 67, 78, 79, 80, 85, 93 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 29, 30, 32, 46, 66, 74, 76, 78, 88, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 26, 28, 46, 61, 68, 74, 77, 80, 87, 89, 94 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 26, 30, 32, 46, 49, 54, 56, 68, 72, 90, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 27, 29, 33, 41, 45, 46, 73, 74, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 29, 46, 48, 51, 53, 58, 60, 68, 71, 74, 87 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 27, 45, 46, 48, 49, 56, 58, 60, 75, 86, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 28, 45, 46, 59, 62, 69, 73, 74, 79, 86, 96 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 28, 46, 48, 55, 66, 71, 74, 82, 84, 88, 92 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 33, 46, 49, 51, 53, 56, 66, 69, 71, 73, 81 ] ]; # Working on Small Group [96, 99]... # There are 12 difference sets: # (Omar found 12) DS96[ 99 ] := [ [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 25, 46, 49, 55, 62, 66, 82, 88, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 34, 46, 48, 49, 68, 71, 80, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 41, 45, 46, 49, 61, 73, 77, 83, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 25, 46, 47, 49, 59, 69, 72, 79, 84, 86, 92 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 25, 33, 37, 47, 48, 50, 57, 63, 70, 73, 78, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 33, 34, 37, 50, 57, 61, 62, 63, 70, 78, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 33, 37, 45, 50, 57, 63, 70, 71, 72, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 33, 37, 50, 57, 59, 63, 70, 78, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 19, 31, 54, 62, 67, 75, 77, 81, 82, 85, 93 ], [ 1, 2, 3, 4, 7, 13, 19, 23, 25, 47, 48, 50, 55, 56, 62, 67, 73, 82, 85, 96 ], [ 1, 2, 3, 4, 7, 13, 19, 25, 27, 50, 53, 54, 55, 56, 62, 67, 78, 82, 85, 96 ], [ 1, 2, 3, 4, 7, 13, 19, 25, 41, 50, 55, 56, 62, 67, 68, 69, 82, 85, 88, 96 ] ]; # 100] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 100 ] := [ ]; # Working on Small Group [96, 101]... # There are 8 difference sets: # (Omar found 8) DS96[ 101 ] := [ [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 26, 46, 50, 55, 61, 66, 83, 88, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 34, 46, 47, 50, 69, 72, 79, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 41, 45, 46, 50, 62, 73, 77, 82, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 26, 46, 48, 50, 59, 68, 71, 80, 84, 87, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 53, 58, 59, 61, 65, 67, 70, 75, 77, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 29, 36, 46, 49, 59, 61, 77, 87, 88, 89, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 29, 36, 41, 45, 46, 49, 55, 62, 73, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 29, 36, 46, 48, 49, 66, 68, 71, 79, 83, 84, 92 ] ]; # [96,102] has [48,36] image (so NO DS) DS96[ 102 ] := [ ]; # Working on Small Group [96, 103]... # There are 40 difference sets: # (Omar found 40) DS96[ 103 ] := [ [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 36, 46, 62, 69, 71, 74, 79, 86, 92, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 36, 46, 66, 71, 74, 79, 83, 84, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 46, 50, 55, 63, 69, 72, 82, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 36, 41, 46, 48, 74, 77, 82, 89, 93, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 36, 41, 46, 72, 73, 74, 80, 82, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 46, 50, 63, 66, 68, 71, 73, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 36, 45, 46, 47, 55, 62, 69, 74, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 36, 45, 46, 47, 55, 66, 74, 83, 84, 88, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 36, 46, 48, 59, 61, 68, 74, 77, 87, 89, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 36, 46, 59, 61, 68, 72, 73, 74, 80, 87, 91 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 41, 45, 46, 48, 50, 61, 63, 80, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 46, 47, 50, 59, 62, 63, 77, 79, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 16, 31, 51, 54, 58, 59, 61, 70, 85, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 51, 54, 58, 59, 61, 65, 70, 80, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 40, 43, 58, 62, 75, 77, 78, 82, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 43, 51, 54, 58, 59, 65, 67, 80, 84, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 36, 54, 58, 59, 61, 64, 70, 76, 77, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 40, 44, 57, 59, 64, 77, 78, 80, 84, 90 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 37, 39, 58, 59, 61, 70, 77, 78, 90, 93 ], [ 1, 2, 3, 4, 7, 13, 16, 23, 24, 26, 29, 30, 32, 47, 48, 70, 73, 76, 78, 85 ], [ 1, 2, 3, 4, 7, 13, 16, 24, 26, 29, 30, 32, 45, 70, 71, 72, 76, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 13, 16, 24, 26, 29, 30, 32, 59, 70, 76, 78, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 24, 26, 29, 46, 59, 61, 68, 80, 87, 89, 96 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 24, 26, 29, 46, 59, 71, 80, 84, 87, 88, 91 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 25, 30, 33, 46, 50, 53, 56, 69, 71, 90, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 45, 46, 47, 62, 69, 77, 82, 93, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 45, 46, 62, 69, 73, 77, 79, 86, 94 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 46, 48, 55, 61, 66, 68, 83, 89, 96 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 26, 29, 46, 48, 55, 66, 71, 83, 84, 88, 91 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 27, 45, 46, 47, 50, 56, 57, 60, 76, 87, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 25, 32, 46, 50, 51, 54, 56, 66, 68, 72, 73, 81 ], [ 1, 2, 3, 4, 7, 16, 23, 26, 28, 36, 47, 48, 49, 61, 64, 70, 73, 93, 94, 96 ], [ 1, 2, 3, 4, 7, 16, 26, 28, 30, 36, 49, 57, 58, 61, 64, 70, 81, 93, 94, 96 ], [ 1, 2, 3, 4, 7, 16, 26, 28, 36, 45, 49, 61, 64, 70, 71, 72, 89, 93, 94, 96 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 27, 35, 46, 51, 56, 58, 60, 69, 72, 74, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 26, 28, 32, 36, 46, 49, 54, 66, 68, 76, 81, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 30, 32, 35, 41, 45, 46, 48, 54, 56, 74, 76, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 33, 35, 46, 47, 53, 56, 66, 74, 75, 81, 88, 89 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 27, 28, 36, 46, 48, 49, 51, 57, 60, 71, 87, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 26, 28, 30, 33, 36, 45, 46, 49, 53, 69, 73, 75, 95 ] ]; # [96,104] has [48,36] image (so NO DS) DS96[ 104 ] := [ ]; # Working on Small Group [96, 105]... # There are 8 difference sets: # (Omar found 6) DS96[ 105 ] := [ [ 1, 2, 3, 4, 7, 9, 16, 23, 24, 25, 33, 35, 47, 48, 57, 65, 70, 73, 75, 78 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 25, 33, 34, 35, 57, 61, 62, 65, 70, 75, 78, 84 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 25, 33, 35, 45, 57, 65, 70, 71, 72, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 24, 25, 33, 35, 57, 59, 65, 70, 75, 78, 82, 83, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 16, 31, 37, 58, 62, 63, 70, 76, 78, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 16, 23, 28, 37, 47, 48, 49, 52, 59, 62, 63, 70, 73, 77, 79 ], [ 1, 2, 3, 4, 7, 16, 28, 30, 37, 49, 52, 57, 58, 59, 62, 63, 70, 77, 79, 81 ], [ 1, 2, 3, 4, 7, 16, 28, 37, 45, 49, 52, 59, 62, 63, 70, 71, 72, 77, 79, 89 ] ]; #106] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 106 ] := [ ]; # [96,107] has [48,5] image (so NO DS) DS96[ 107 ] := [ ]; # 108] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 108 ] := [ ]; # [96,109] has both [48,6] and [48,36] images (so NO DS) DS96[ 109 ] := [ ]; # [96,110] has both [48,7] and [48,36] images (so NO DS) DS96[ 110 ] := [ ]; # [96,111] has [48,36] image (so NO DS) DS96[ 111 ] := [ ]; # [96,112] has [48,36] image (so NO DS) DS96[ 112 ] := [ ]; #113] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 113 ] := [ ]; #114] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 114 ] := [ ]; # [96,115] has [48,36] image (so NO DS) DS96[ 115 ] := [ ]; # [96,116] has [48,36] image (so NO DS) DS96[ 116 ] := [ ]; # 117] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 117 ] := [ ]; # 118] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 118 ] := [ ]; # 119] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 119 ] := [ ]; # 120] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 120 ] := [ ]; # 121] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 121 ] := [ ]; # 122] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 122 ] := [ ]; # 123] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 123 ] := [ ]; # 124] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 124 ] := [ ]; # 125] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 125 ] := [ ]; # 126] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 126 ] := [ ]; # [96,127] has [48,9] image (so NO DS) DS96[ 127 ] := [ ]; # 128] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 128 ] := [ ]; # Working on Small Group [96, 129]... # There are 36 difference sets: # (Omar found 32) DS96[ 129 ] := [ [ 1, 2, 3, 4, 7, 8, 12, 19, 29, 32, 33, 35, 60, 61, 65, 67, 74, 80, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 12, 19, 32, 33, 35, 50, 56, 60, 62, 65, 67, 79, 82, 96 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 29, 30, 35, 46, 47, 69, 74, 76, 78, 86, 89 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 35, 45, 46, 48, 50, 56, 57, 68, 78, 87, 90 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 29, 32, 35, 47, 48, 54, 65, 67, 73, 74, 75, 81 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 29, 35, 47, 48, 61, 65, 67, 73, 74, 80, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 32, 34, 35, 54, 61, 62, 65, 67, 74, 75, 81, 84 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 32, 35, 41, 54, 65, 67, 68, 69, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 32, 35, 54, 55, 65, 67, 74, 75, 79, 80, 81, 93 ], [ 1, 2, 3, 4, 7, 8, 19, 29, 35, 41, 61, 65, 67, 68, 69, 74, 80, 88, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 29, 32, 35, 46, 51, 54, 58, 71, 74, 88, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 29, 35, 46, 61, 66, 72, 74, 80, 82, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 29, 33, 35, 41, 46, 51, 53, 58, 71, 73, 74, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 29, 34, 35, 45, 46, 47, 69, 74, 87, 91, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 29, 35, 41, 46, 62, 66, 72, 73, 74, 79, 82, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 29, 35, 45, 46, 48, 55, 68, 74, 84, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 23, 46, 52, 53, 69, 74, 76, 81, 86, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 41, 46, 48, 52, 53, 71, 74, 76, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 45, 46, 52, 53, 68, 73, 74, 76, 81, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 46, 47, 52, 53, 66, 72, 74, 76, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 22, 23, 31, 32, 39, 56, 67, 69, 76, 86, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 22, 31, 32, 39, 41, 48, 56, 67, 71, 76, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 22, 31, 32, 39, 45, 56, 67, 68, 73, 76, 87, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 22, 31, 32, 39, 47, 56, 66, 67, 72, 76, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 23, 40, 47, 48, 52, 53, 64, 70, 73, 74, 76, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 34, 40, 56, 62, 64, 70, 76, 79, 90, 93 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 40, 55, 56, 61, 64, 70, 76, 80, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 40, 56, 59, 64, 70, 76, 83, 90, 91, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 40, 56, 64, 70, 76, 77, 82, 90, 92, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 40, 41, 52, 53, 64, 68, 69, 70, 74, 76, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 36, 43, 49, 52, 60, 62, 79, 85, 92, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 36, 49, 52, 60, 61, 64, 70, 80, 83, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 27, 32, 45, 46, 52, 58, 68, 73, 74, 87, 90 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 27, 32, 46, 47, 52, 58, 66, 72, 74, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 36, 47, 48, 49, 52, 54, 58, 64, 70, 73, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 36, 45, 49, 52, 54, 58, 64, 70, 71, 72, 89, 90 ] ]; # Working on Small Group [96, 130]... # There are 88 difference sets: # (Omar found 4) DS96[ 130 ] := [ [ 1, 2, 3, 4, 7, 8, 12, 19, 28, 32, 33, 36, 39, 60, 62, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 12, 19, 32, 33, 36, 39, 49, 56, 59, 60, 80, 84, 85, 96 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 28, 36, 45, 46, 48, 51, 53, 74, 81, 88, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 30, 36, 45, 46, 49, 53, 56, 69, 73, 90, 95 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 28, 36, 39, 47, 48, 54, 58, 60, 73, 74, 75, 85 ], [ 1, 2, 3, 4, 7, 8, 19, 23, 28, 36, 39, 47, 48, 62, 73, 74, 77, 85, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 34, 36, 39, 54, 58, 60, 61, 62, 74, 75, 84, 85 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 36, 39, 41, 54, 58, 60, 68, 69, 74, 75, 85, 88 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 36, 39, 41, 62, 68, 69, 74, 77, 85, 88, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 19, 28, 36, 39, 54, 55, 58, 60, 74, 75, 79, 80, 85, 93 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 28, 30, 33, 36, 46, 66, 68, 74, 78, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 28, 36, 46, 59, 68, 72, 74, 80, 84, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 30, 36, 41, 46, 47, 54, 60, 66, 74, 89, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 34, 36, 45, 46, 69, 73, 74, 79, 83, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 36, 41, 46, 47, 59, 62, 72, 74, 86, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 28, 36, 45, 46, 48, 55, 61, 74, 83, 88, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 23, 46, 52, 54, 68, 74, 75, 81, 87, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 41, 46, 47, 52, 54, 72, 74, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 45, 46, 52, 54, 69, 73, 74, 75, 81, 86 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 22, 46, 48, 52, 54, 66, 71, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 23, 31, 33, 40, 56, 67, 68, 75, 87, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 31, 33, 40, 41, 47, 56, 67, 72, 75, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 31, 33, 40, 45, 56, 67, 69, 73, 75, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 21, 31, 33, 40, 48, 56, 66, 67, 71, 75, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 23, 39, 47, 48, 52, 54, 65, 70, 73, 74, 75, 81 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 34, 39, 54, 56, 62, 65, 70, 78, 91, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 39, 54, 55, 56, 65, 70, 78, 80, 82, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 39, 54, 56, 59, 65, 70, 78, 79, 83, 93 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 32, 39, 54, 56, 61, 65, 70, 77, 78, 84, 92 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 33, 39, 45, 56, 65, 70, 71, 75, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 33, 39, 56, 59, 65, 70, 75, 82, 90, 92, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 33, 39, 56, 65, 66, 70, 72, 75, 86, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 31, 33, 39, 56, 65, 70, 75, 77, 83, 90, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 41, 52, 54, 65, 68, 69, 70, 74, 75, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 45, 52, 54, 65, 70, 71, 72, 74, 75, 81, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 13, 39, 52, 54, 65, 66, 70, 74, 75, 81, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 35, 44, 50, 52, 60, 61, 80, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 35, 50, 52, 60, 62, 65, 70, 79, 82, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 27, 33, 46, 52, 57, 68, 74, 87, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 23, 46, 52, 55, 62, 68, 74, 82, 87, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 27, 33, 41, 46, 47, 52, 57, 72, 74, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 27, 33, 45, 46, 52, 57, 69, 73, 74, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 27, 33, 46, 48, 52, 57, 66, 71, 74, 88, 90 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 34, 45, 46, 52, 69, 73, 74, 80, 86, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 34, 46, 48, 52, 66, 71, 74, 80, 88, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 22, 41, 46, 47, 52, 55, 62, 72, 74, 82, 95, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 23, 27, 31, 40, 54, 56, 57, 67, 68, 81, 87, 89 ], [ 1, 2, 3, 4, 7, 9, 13, 21, 27, 31, 40, 41, 47, 54, 56, 57, 67, 72, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 13, 27, 31, 39, 54, 56, 57, 59, 65, 70, 81, 82, 92, 96 ], [ 1, 2, 3, 4, 7, 9, 13, 27, 31, 39, 54, 56, 57, 65, 70, 77, 81, 83, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 35, 44, 47, 48, 50, 52, 54, 73, 75, 81, 85 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 33, 35, 47, 48, 50, 52, 53, 57, 65, 70, 73, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 30, 35, 44, 50, 52, 57, 58, 61, 80, 81, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 30, 35, 50, 52, 57, 58, 62, 65, 70, 79, 81, 82, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 35, 44, 45, 50, 52, 54, 71, 72, 75, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 9, 16, 33, 35, 45, 50, 52, 53, 57, 65, 70, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 44, 54, 75, 81, 82, 85, 92, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 44, 57, 76, 78, 80, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 54, 55, 75, 81, 83, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 54, 59, 61, 75, 80, 81, 85, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 54, 62, 75, 77, 79, 81, 85, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 55, 57, 62, 76, 78, 82, 85, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 57, 59, 76, 78, 79, 84, 85, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 57, 61, 76, 77, 78, 83, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 12, 13, 26, 33, 34, 39, 44, 52, 57, 81, 84, 85, 91, 92 ], [ 1, 2, 3, 4, 7, 10, 12, 13, 26, 33, 39, 44, 52, 55, 57, 81, 82, 83, 85, 93 ], [ 1, 2, 3, 4, 7, 10, 12, 13, 26, 33, 39, 44, 52, 57, 59, 79, 80, 81, 85, 94 ], [ 1, 2, 3, 4, 7, 10, 12, 13, 26, 33, 39, 44, 52, 57, 61, 62, 77, 81, 85, 96 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 21, 23, 28, 40, 56, 60, 67, 68, 72, 75, 76, 95 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 21, 28, 40, 41, 47, 56, 60, 67, 75, 76, 87, 89 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 21, 28, 40, 45, 48, 56, 60, 67, 75, 76, 86, 88 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 21, 28, 40, 56, 60, 66, 67, 69, 71, 73, 75, 76 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 28, 39, 44, 45, 56, 60, 71, 75, 76, 85, 87, 95 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 28, 39, 44, 56, 59, 60, 75, 76, 82, 85, 92, 96 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 28, 39, 44, 56, 60, 66, 72, 75, 76, 85, 86, 89 ], [ 1, 2, 3, 4, 7, 11, 12, 13, 28, 39, 44, 56, 60, 75, 76, 77, 83, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 11, 13, 21, 23, 27, 28, 40, 56, 57, 58, 67, 68, 72, 78, 95 ], [ 1, 2, 3, 4, 7, 11, 13, 21, 27, 28, 40, 41, 47, 56, 57, 58, 67, 78, 87, 89 ], [ 1, 2, 3, 4, 7, 11, 13, 27, 28, 39, 44, 56, 57, 58, 59, 78, 82, 85, 92, 96 ], [ 1, 2, 3, 4, 7, 11, 13, 27, 28, 39, 44, 56, 57, 58, 77, 78, 83, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 45, 58, 65, 70, 71, 72, 74, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 58, 65, 66, 70, 74, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 28, 39, 44, 45, 50, 52, 54, 71, 72, 75, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 28, 39, 44, 50, 52, 54, 66, 75, 81, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 26, 27, 28, 46, 57, 60, 68, 74, 76, 87, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 26, 28, 46, 55, 68, 74, 82, 84, 87, 89, 92 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 27, 28, 41, 46, 47, 57, 60, 72, 74, 76, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 26, 28, 41, 46, 47, 55, 72, 74, 82, 84, 92, 95 ] ]; # Working on Small Group [96, 131]... # There are 40 difference sets: # (Omar found 40) DS96[ 131 ] := [ [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 35, 50, 52, 60, 62, 65, 70, 79, 82, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 36, 49, 52, 60, 62, 64, 70, 77, 79, 82 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 35, 46, 50, 52, 53, 58, 68, 71, 73, 76, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 36, 46, 49, 52, 53, 57, 68, 72, 73, 76, 87 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 25, 44, 47, 48, 50, 54, 57, 60, 63, 64, 73, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 36, 47, 48, 49, 52, 54, 58, 64, 70, 73, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 33, 35, 47, 48, 50, 52, 53, 57, 65, 70, 73, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 35, 47, 48, 50, 52, 62, 65, 70, 73, 79, 82, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 36, 47, 48, 49, 52, 62, 64, 70, 73, 77, 79, 82 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 34, 44, 50, 54, 57, 60, 61, 62, 63, 64, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 44, 45, 50, 54, 57, 60, 63, 64, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 25, 44, 50, 54, 57, 59, 60, 63, 64, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 30, 35, 50, 52, 57, 58, 62, 65, 70, 79, 81, 82, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 30, 36, 49, 52, 57, 58, 62, 64, 70, 77, 79, 81, 82 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 34, 36, 49, 52, 54, 58, 61, 62, 64, 70, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 36, 45, 49, 52, 54, 58, 64, 70, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 36, 49, 52, 54, 58, 59, 64, 70, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 33, 34, 35, 50, 52, 53, 57, 61, 62, 65, 70, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 33, 35, 45, 50, 52, 53, 57, 65, 70, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 33, 35, 50, 52, 53, 57, 59, 65, 70, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 35, 45, 50, 52, 62, 65, 70, 71, 72, 79, 82, 89, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 36, 45, 49, 52, 62, 64, 70, 71, 72, 77, 79, 82, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 46, 50, 62, 63, 66, 69, 71, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 54, 57, 60, 69, 72, 75, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 55, 61, 69, 72, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 36, 46, 49, 52, 54, 58, 60, 69, 71, 75, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 36, 46, 49, 52, 62, 69, 71, 77, 86, 93, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 41, 46, 48, 50, 63, 82, 87, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 45, 46, 47, 50, 55, 63, 83, 84, 86, 88, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 46, 50, 59, 61, 63, 68, 72, 73, 77, 80, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 27, 30, 32, 36, 41, 46, 48, 49, 52, 89, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 27, 32, 35, 41, 45, 46, 48, 50, 52, 81, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 30, 33, 35, 46, 47, 50, 51, 52, 66, 78, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 33, 36, 45, 46, 47, 49, 51, 52, 66, 78, 81, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 46, 47, 50, 52, 66, 79, 83, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 36, 41, 46, 48, 49, 52, 79, 82, 89, 92, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 41, 45, 46, 48, 50, 52, 80, 82, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 46, 50, 52, 59, 62, 68, 71, 73, 77, 87, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 36, 45, 46, 47, 49, 52, 66, 80, 83, 84, 88, 91 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 36, 46, 49, 52, 55, 59, 61, 68, 72, 73, 87, 96 ] ]; # [96,132] has [48,36] image (so NO DS) DS96[ 132 ] := [ ]; # Working on Small Group [96, 133]... # There are 16 difference sets: # (Omar found 16) DS96[ 133 ] := [ [ 1, 2, 3, 4, 7, 8, 12, 16, 32, 33, 35, 44, 50, 56, 60, 83, 84, 85, 93, 96 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 30, 35, 46, 48, 50, 56, 68, 71, 76, 78, 95 ], [ 1, 2, 3, 4, 7, 8, 16, 23, 24, 28, 30, 35, 44, 47, 48, 60, 73, 75, 78, 85 ], [ 1, 2, 3, 4, 7, 8, 16, 24, 28, 30, 35, 44, 45, 60, 71, 72, 75, 78, 85, 89 ], [ 1, 2, 3, 4, 7, 8, 16, 24, 28, 30, 35, 44, 59, 60, 75, 78, 82, 83, 85, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 28, 35, 46, 59, 62, 79, 86, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 28, 35, 41, 45, 46, 61, 73, 80, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 28, 35, 46, 47, 55, 66, 69, 72, 82, 84, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 36, 43, 49, 52, 55, 60, 83, 84, 85, 96 ], [ 1, 2, 3, 4, 7, 9, 12, 16, 32, 33, 36, 49, 52, 60, 62, 64, 70, 77, 79, 82 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 32, 36, 47, 48, 49, 52, 54, 58, 64, 70, 73, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 23, 36, 43, 47, 48, 49, 52, 55, 73, 83, 84, 85, 96 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 34, 36, 49, 52, 54, 58, 61, 62, 64, 70, 84, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 36, 45, 49, 52, 54, 58, 64, 70, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 16, 32, 36, 49, 52, 54, 58, 59, 64, 70, 82, 83, 90, 94 ], [ 1, 2, 3, 4, 7, 9, 16, 36, 43, 45, 49, 52, 55, 71, 72, 83, 84, 85, 89, 96 ] ]; # [96,134] has [48,36] image (so NO DS) DS96[ 134 ] := [ ]; # Working on Small Group [96, 135]... # There are 12 difference sets: # (Omar found 12) DS96[ 135 ] := [ [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 51, 58, 78, 80, 82, 84, 85, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 35, 40, 53, 58, 61, 76, 80, 85, 91, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 19, 31, 40, 55, 61, 63, 64, 77, 78, 81, 83, 90 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 29, 35, 40, 47, 48, 52, 54, 57, 60, 73, 75, 85 ], [ 1, 2, 3, 4, 7, 19, 23, 24, 29, 35, 40, 47, 48, 52, 55, 61, 73, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 19, 23, 25, 40, 47, 48, 49, 56, 61, 63, 64, 73, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 19, 24, 27, 29, 35, 40, 52, 53, 54, 55, 61, 78, 85, 94, 96 ], [ 1, 2, 3, 4, 7, 19, 24, 29, 35, 40, 41, 52, 54, 57, 60, 68, 69, 75, 85, 88 ], [ 1, 2, 3, 4, 7, 19, 24, 29, 35, 40, 41, 52, 55, 61, 68, 69, 85, 88, 94, 96 ], [ 1, 2, 3, 4, 7, 19, 24, 29, 35, 40, 52, 54, 55, 57, 60, 75, 79, 80, 85, 93 ], [ 1, 2, 3, 4, 7, 19, 25, 27, 40, 49, 53, 54, 56, 61, 63, 64, 78, 80, 83, 92 ], [ 1, 2, 3, 4, 7, 19, 25, 40, 41, 49, 56, 61, 63, 64, 68, 69, 80, 83, 88, 92 ] ]; # Working on Small Group [96, 136]... # There are 8 difference sets: # (Omar found 8) DS96[ 136 ] := [ [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 35, 46, 62, 69, 71, 79, 87, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 34, 35, 41, 46, 48, 66, 82, 89, 93, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 45, 46, 47, 55, 77, 83, 84, 88, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 46, 59, 61, 68, 72, 73, 80, 86, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 36, 40, 43, 51, 53, 61, 64, 80, 81, 92, 94 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 24, 25, 27, 36, 46, 51, 56, 57, 60, 69, 71, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 30, 33, 36, 45, 46, 47, 53, 56, 66, 75, 88 ], [ 1, 2, 3, 4, 7, 21, 22, 24, 25, 32, 36, 41, 46, 48, 54, 56, 76, 81, 89, 95 ] ]; # [96,137] has [48,36] image (so NO DS), verified by BruteForceSieve on May 15, 2006 DS96[ 137 ] := [ ]; # 138] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 138 ] := [ ]; # 139] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 139 ] := [ ]; # 140] -- Omar says NO, verified by BruteForceSieve on May 15, 2006 DS96[ 140 ] := [ ]; # Working on Small Group [96, 141]... # There are 60 difference sets: # (Omar found 60) DS96[ 141 ] := [ [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 35, 45, 46, 47, 50, 54, 56, 58, 75, 88, 95 ], [ 1, 2, 3, 4, 7, 8, 12, 21, 22, 35, 46, 47, 50, 54, 56, 57, 66, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 46, 56, 59, 61, 63, 69, 72, 91, 93, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 24, 46, 56, 61, 63, 66, 69, 71, 92, 93, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 30, 32, 35, 46, 50, 56, 69, 72, 78, 86, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 23, 32, 35, 46, 50, 51, 56, 69, 71, 78, 81, 87 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 34, 45, 46, 47, 56, 63, 80, 83, 86, 88, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 34, 46, 47, 56, 63, 77, 80, 82, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 41, 45, 46, 48, 56, 63, 79, 83, 84, 86, 96 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 41, 46, 48, 56, 63, 77, 79, 82, 84, 87, 89 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 46, 55, 56, 59, 62, 63, 68, 72, 73, 91, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 24, 46, 55, 56, 62, 63, 66, 68, 71, 73, 92, 94 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 27, 30, 33, 35, 46, 50, 56, 68, 72, 73, 86, 90 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 27, 33, 35, 46, 50, 51, 56, 68, 71, 73, 81, 87 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 35, 41, 45, 46, 48, 50, 53, 56, 58, 60, 75, 95 ], [ 1, 2, 3, 4, 7, 8, 21, 22, 35, 41, 46, 48, 50, 53, 56, 57, 60, 66, 76, 89 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 44, 54, 57, 77, 85, 90, 93, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 39, 54, 57, 65, 70, 83, 90, 91, 93 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 40, 43, 51, 78, 79, 81, 83, 85, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 34, 43, 54, 65, 67, 75, 79, 81, 83, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 39, 44, 54, 57, 61, 80, 83, 85, 90, 91 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 13, 31, 40, 43, 51, 55, 61, 78, 81, 85, 92, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 37, 40, 57, 70, 78, 79, 83, 90, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 37, 44, 54, 57, 67, 76, 79, 94, 96 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 39, 44, 54, 57, 65, 76, 91, 93, 94 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 34, 35, 40, 43, 65, 75, 78, 79, 81, 83, 92 ], [ 1, 2, 3, 4, 7, 10, 11, 12, 31, 35, 40, 44, 55, 57, 61, 64, 78, 83, 90, 92 ], [ 1, 2, 3, 4, 7, 12, 13, 24, 40, 41, 43, 52, 53, 56, 58, 68, 69, 85, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 13, 24, 40, 43, 45, 52, 53, 56, 58, 71, 72, 85, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 13, 24, 40, 43, 52, 53, 56, 58, 66, 85, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 41, 44, 51, 68, 69, 74, 78, 81, 85, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 41, 58, 65, 68, 69, 70, 74, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 44, 45, 51, 71, 72, 74, 78, 81, 85, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 44, 51, 66, 74, 78, 81, 85, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 45, 58, 65, 70, 71, 72, 74, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 28, 39, 58, 65, 66, 70, 74, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 41, 43, 49, 53, 56, 58, 65, 67, 68, 69, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 43, 45, 49, 53, 56, 58, 65, 67, 71, 72, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 13, 26, 43, 49, 53, 56, 58, 65, 66, 67, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 37, 40, 41, 43, 63, 68, 69, 78, 81, 88, 90 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 37, 40, 43, 45, 63, 71, 72, 78, 81, 89, 90 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 37, 40, 43, 63, 66, 78, 81, 86, 87, 90, 95 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 41, 57, 63, 65, 68, 69, 70, 75, 78, 88 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 45, 57, 63, 65, 70, 71, 72, 75, 78, 89 ], [ 1, 2, 3, 4, 7, 12, 24, 25, 29, 40, 57, 63, 65, 66, 70, 75, 78, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 25, 41, 44, 49, 51, 54, 56, 57, 63, 65, 67, 68, 69, 88 ], [ 1, 2, 3, 4, 7, 12, 25, 44, 45, 49, 51, 54, 56, 57, 63, 65, 67, 71, 72, 89 ], [ 1, 2, 3, 4, 7, 12, 25, 44, 49, 51, 54, 56, 57, 63, 65, 66, 67, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 12, 35, 40, 41, 43, 49, 52, 53, 56, 58, 65, 68, 69, 76, 88 ], [ 1, 2, 3, 4, 7, 12, 35, 40, 43, 45, 49, 52, 53, 56, 58, 65, 71, 72, 76, 89 ], [ 1, 2, 3, 4, 7, 12, 35, 40, 43, 49, 52, 53, 56, 58, 65, 66, 76, 86, 87, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 24, 30, 32, 46, 52, 56, 68, 72, 76, 78, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 23, 24, 46, 52, 55, 56, 61, 69, 71, 92, 94, 95 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 27, 33, 46, 52, 56, 66, 69, 71, 73, 75, 81 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 41, 46, 48, 52, 56, 77, 80, 82, 84, 86, 89 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 45, 46, 48, 51, 52, 53, 56, 58, 60, 86, 88 ], [ 1, 2, 3, 4, 7, 13, 21, 22, 24, 46, 52, 56, 59, 62, 66, 68, 72, 73, 91, 93 ], [ 1, 2, 3, 4, 7, 21, 22, 23, 25, 30, 32, 35, 46, 54, 56, 69, 72, 74, 76, 86 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 27, 35, 41, 45, 46, 48, 51, 56, 58, 60, 74, 95 ], [ 1, 2, 3, 4, 7, 21, 22, 25, 33, 35, 46, 53, 56, 68, 71, 73, 74, 75, 81, 87 ] ]; # Working on Small Group [96, 142]... # There are 64 difference sets: # (Omar found 64) DS96[ 142 ] := [ [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 41, 46, 48, 71, 75, 78, 81, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 47, 51, 58, 66, 78, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 25, 35, 46, 51, 58, 68, 71, 73, 78, 87 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 24, 46, 51, 52, 53, 58, 63, 66, 68, 71, 73 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 25, 36, 41, 46, 48, 71, 74, 76, 78, 81, 86 ], [ 1, 2, 3, 4, 7, 9, 12, 21, 22, 25, 36, 46, 47, 72, 74, 76, 78, 81, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 27, 35, 46, 57, 60, 69, 72, 86, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 32, 35, 46, 54, 69, 72, 75, 81, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 33, 35, 46, 53, 57, 66, 69, 89, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 35, 46, 55, 69, 72, 82, 84, 86, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 25, 35, 46, 61, 69, 72, 80, 86, 91, 94 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 24, 46, 52, 54, 57, 60, 63, 69, 72, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 32, 36, 46, 54, 58, 69, 74, 89, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 33, 36, 46, 51, 53, 57, 69, 74, 89, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 25, 46, 50, 55, 63, 69, 72, 82, 84, 91, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 62, 66, 69, 82, 89, 91, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 23, 35, 46, 50, 52, 69, 72, 80, 82, 84, 86, 91 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 27, 30, 35, 46, 47, 60, 72, 76, 86, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 27, 35, 41, 45, 46, 48, 57, 60, 90, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 33, 35, 46, 47, 53, 66, 76, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 30, 33, 35, 46, 53, 68, 71, 73, 76, 87 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 41, 45, 46, 48, 54, 75, 81, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 32, 35, 45, 46, 51, 54, 58, 68, 73, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 34, 35, 46, 47, 66, 77, 83, 88, 89, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 34, 35, 46, 68, 71, 73, 77, 83, 87, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 41, 45, 46, 48, 55, 82, 84, 95, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 41, 45, 46, 48, 61, 80, 91, 94, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 46, 47, 59, 62, 66, 79, 88, 89, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 25, 35, 46, 59, 62, 68, 71, 73, 79, 87, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 27, 32, 41, 45, 46, 48, 52, 63, 75, 81, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 24, 30, 33, 46, 47, 52, 63, 76, 78, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 27, 30, 36, 41, 46, 48, 60, 71, 74, 75, 86 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 27, 30, 36, 46, 47, 60, 72, 74, 75, 87, 88 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 32, 36, 45, 46, 54, 58, 66, 68, 73, 74, 90 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 33, 36, 45, 46, 51, 53, 57, 66, 68, 73, 74 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 34, 46, 50, 63, 66, 68, 71, 73, 83, 92, 93 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 41, 45, 46, 48, 50, 61, 63, 80, 86, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 25, 46, 47, 50, 59, 62, 63, 77, 79, 87, 88, 89 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 41, 46, 48, 50, 52, 71, 79, 87, 94, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 34, 35, 46, 50, 52, 68, 71, 73, 79, 83, 87, 92 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 41, 45, 46, 48, 50, 52, 55, 61, 94, 95, 96 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 45, 46, 50, 52, 55, 61, 68, 73, 83, 92, 95 ], [ 1, 2, 3, 4, 7, 9, 21, 22, 35, 46, 47, 50, 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51, 58, 6