# Database of various difference sets with order (n=k-lambda) at least 16,
# created to be convenient for GAP. (Download this as a text file.)

# Omar AbuGhneim and Ken Smith, 
# Last modified April 22, 2006.

# There is a separate file with approximately 1800 difference sets
# with parameters (96,20,4).  There will soon be a file of difference
# sets with parameters (64,28,12).

# Each line has 3 entries:  the parameters [v,k,lambda],
# the GAP catalogue number [v,cn], and then the index set I
# for which the difference set is 
# { Elements( SmallGroup( v, cn ) )[i]  : i in I }.

# Last modified, April 17, 2006.

#     To run this program, save it as "DifSetDatabase_order_ge_16.txt"
# in the same folder as Gap.  Then insert the following 
# Read statement at a GAP command line (after removing the "#gap>"):

#gap>  Read("DifSetDatabase_order_ge_16.txt");

# Then, for a given member of the database, say
#gap> DS := DifSetDatabase[ <number> ];
# define the difference set by:
#gap> e := Elements( SmallGroup( DS[2][1], DS[2][2] ) );
#gap> difset := DS[3];

# Each difference set listed is the "lexicographically least" 
# of all equivalent difference sets.
# (In this ordering, [1,2,4] < [1,2,5] < [1,3,4] < [2,3,4].)

# Order 16
# (parameters (96,20,4) and (64, 28, 12) are in a different file)
[ [ 273, 17, 1 ], [ 273, 5 ], [ 1, 2, 9, 32, 38, 44, 65, 76, 85, 101, 139, 157, 178, 187, 206, 209, 221 ] ],
 
[ [ 85, 21, 5 ], [ 85, 1 ], [ 1, 2, 3, 4, 7, 9, 11, 14, 27, 28, 30, 37, 43, 45, 48, 62, 63, 69, 72, 74, 75 ] ],

[ [ 63, 31, 15 ], [ 63, 4 ], [ 1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 16, 18, 23, 24, 26, 27, 29, 30, 31, 34, 36, 37, 41, 45, 47, 49, 50, 54, 55, 57, 60 ] ], 
[ [ 63, 31, 15 ], [ 63, 2 ], [ 1, 2, 3, 4, 5, 6, 10, 11, 12, 13, 14, 16, 17, 21, 22, 23, 24, 28, 31, 33, 39, 40, 41, 45, 47, 49, 51, 52, 53, 55, 63 ] ], 


# Order 17
[ [ 307, 18, 1 ], [ 307, 1 ], [ 1, 2, 4, 22, 26, 32, 69, 78, 92, 171, 178, 186, 197, 213, 226, 258, 270, 275 ] ], 

[ [ 67, 33, 16 ], [ 67, 1 ], [ 1, 2, 3, 4, 5, 6, 8, 10, 11, 12, 13, 17, 18, 21, 23, 26, 29, 30, 32, 34, 35, 38, 39, 40, 45, 47, 54, 55, 57, 58, 59, 61, 65 ] ], 


# Order 18
[ [ 71, 35, 17 ], [ 71, 1 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 19, 20, 24, 25, 27, 29, 30, 32, 36, 37, 38, 40, 43, 45, 48, 49, 50, 54, 57, 58, 60, 64 ] ], 


# Order 19
[ [ 381, 20, 1 ], [ 381, 2 ], [ 1, 2, 3, 19, 57, 85, 91, 110, 128, 133, 137, 149, 169, 184, 214, 281, 289, 321, 350, 376 ] ], 

[ [ 101, 25, 6 ], [ 101, 1 ], [ 1, 2, 3, 4, 7, 10, 11, 15, 18, 20, 25, 29, 40, 43, 48, 49, 55, 60, 61, 76, 78, 80, 82, 92, 95 ] ], 


# Order 20
[ [ 79, 39, 19 ], [ 79, 1 ], [ 1, 2, 3, 4, 5, 6, 8, 9, 14, 15, 19, 21, 23, 25, 27, 28, 29, 32, 33, 34, 35, 38, 45, 47, 48, 50, 55, 56, 59, 63, 64, 66, 67, 70, 71, 72, 73, 75, 78 ] ],

# Order 21
[ [ 109, 28, 7 ], [ 109, 1 ], [ 1, 2, 3, 4, 5, 8, 11, 13, 14, 18, 23, 25, 32, 37, 38, 41, 45, 49, 53, 55, 63, 66, 68, 74, 79, 88, 94, 95 ] ], 

[ [ 83, 41, 20 ], [ 83, 1 ], [ 1, 2, 3, 4, 5, 6, 7, 9, 11, 15, 16, 20, 21, 22, 23, 25, 28, 29, 31, 34, 37, 38, 40, 45, 46, 47, 50, 51, 52, 54, 56, 64, 66, 67, 71, 74, 75, 77, 78, 79, 82 ] ], 


# Order 23
[ [ 553, 24, 1 ], [ 553, 1 ], [ 1, 2, 3, 9, 23, 50, 59, 62, 102, 125, 134, 160, 163, 184, 255, 287, 310, 315, 367, 375, 401, 452, 497, 498 ] ], 


# Order 25
[ [ 651, 26, 1 ], [ 651, 5 ], [ 1, 2, 9, 22, 35, 75, 82, 92, 118, 121, 156, 175, 204, 238, 257, 280, 317, 364, 417, 426, 451, 526, 536, 542, 624, 635 ] ], 

[ [ 156, 31, 6 ], [ 156, 6 ], [ 1, 2, 3, 4, 5, 9, 11, 20, 28, 34, 40, 47, 51, 55, 56, 62, 69, 81, 83, 85, 86, 97, 111, 115, 122, 131, 140, 142, 145, 147, 154 ] ], 

[ [ 99, 49, 24 ], [ 99, 2 ], [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 14, 18, 19, 21, 24, 25, 26, 27, 29, 31, 32, 33, 35, 36, 41, 42, 44, 50, 57, 61, 65, 66, 67, 70, 72, 74, 75, 76, 78, 79, 80, 83, 85, 86, 92, 95, 97, 98 ] ], 

[ [ 175, 30, 5 ], [ 175, 2 ], [ 1, 2, 4, 5, 9, 10, 11, 18, 20, 21, 29, 32, 35, 50, 54, 64, 65, 92, 93, 106, 108, 124, 141, 144, 146, 148, 150, 151, 153, 157 ] ], 

[ [ 133, 33, 8 ], [ 133, 1 ], [ 1, 2, 3, 4, 5, 7, 16, 22, 24, 26, 31, 35, 39, 40, 41, 50, 51, 61, 63, 64, 66, 69, 80, 85, 94, 101, 108, 115, 116, 122, 125, 129, 130 ] ], 


# Order 26
[ [ 103, 51, 25 ], [ 103, 1 ], [ 1, 2, 3, 4, 5, 6, 7, 11, 12, 13, 16, 18, 19, 23, 25, 26, 30, 31, 32, 40, 41, 42, 44, 47, 51, 55, 57, 59, 60, 62, 63, 64, 65, 67, 68, 71, 73, 74, 77, 82, 85, 87, 89, 90, 91, 93, 94, 95, 97, 98, 100 ] ], 


# Order 27
[ [ 757, 28, 1 ], [ 757, 1 ], [ 1, 2, 4, 10, 28, 44, 82, 130, 174, 221, 244, 311, 388, 405, 410, 446, 456, 467, 471, 506, 520, 579, 609, 642, 654, 661, 674, 730 ] ], 

[ [ 121, 40, 13 ], [ 121, 1 ], [ 1, 2, 3, 4, 5, 7, 9, 14, 19, 21, 27, 30, 32, 33, 36, 38, 39, 41, 46, 47, 53, 55, 58, 61, 64, 68, 69, 70, 71, 77, 81, 82, 85, 90, 95, 102, 103, 112, 113, 118 ] ], 
# There are more of these... see Baumert

[ [ 107, 53, 26 ], [ 107, 1 ], [ 1, 2, 3, 4, 5, 6, 8, 11, 15, 17, 19, 21, 22, 25, 26, 27, 28, 29, 31, 32, 33, 34, 36, 39, 40, 41, 44, 45, 48, 49, 53, 54, 56, 61, 67, 68, 71, 73, 75, 77, 78, 79, 81, 82, 84, 91, 92, 93, 94, 97, 100, 102, 103 ] ], 
# Order 29
[ [ 871, 30, 1 ], [ 871, 1 ], [ 1, 2, 3, 9, 31, 65, 85, 109, 170, 174, 184, 278, 318, 355, 370, 378, 483, 485, 502, 534, 546, 561, 608, 680, 722, 733, 790, 817, 820, 843 ] ]


];