The designs, resolvable designs, and their resolutions with a nontrivial automorphism group are available through the links on the table entries. See below for a description of the file format.
| |Aut(D)| | Resolvable designs |
|---|---|
| 1 | 314 263 |
| 2 | 9 588 |
| 3 | 88 |
| 4 | 661 |
| 5 | 3 |
| 6 | 94 |
| 8 | 158 |
| 10 | 7 |
| 12 | 37 |
| 16 | 73 |
| 18 | 2 |
| 24 | 22 |
| 32 | 32 |
| 36 | 2 |
| 48 | 9 |
| 64 | 5 |
| 72 | 1 |
| 96 | 5 |
| 120 | 2 |
| 128 | 1 |
| 192 | 2 |
| 256 | 1 |
| 384 | 2 |
| 768 | 1 |
| 1152 | 1 |
| 1920 | 1 |
| 5760 | 1 |
| Total | 325 062 |
All the 10799 resolvable designs with a nontrivial automorphism group [res1642.txt.gz, gzip-compressed 1.4MB].
| |Aut(D)| | Designs |
|---|---|
| 1 | 19 063 352 |
| 2 | 7 619 |
| 3 | 1 651 |
| 4 | 113 |
| 6 | 53 |
| 12 | 10 |
| 13 | 1 |
| 39 | 2 |
| 156 | 1 |
| Total | 19 072 802 |
All the 9450 designs with a nontrivial automorphism group [d1365.txt.gz, gzip-compressed 0.4MB].
| |Aut(D)| | Designs |
|---|---|
| 1 | 15 097 318 |
| 2 | 10 934 |
| 3 | 2 514 |
| 4 | 143 |
| 6 | 98 |
| 12 | 5 |
| 13 | 2 |
| 39 | 4 |
| 78 | 1 |
| Total | 15 111 019 |
All the 13701 designs with a nontrivial automorphism group [d1476.txt.gz, gzip-compressed 0.6MB].
The design data files are in ASCII format suitable for the GAP toolkit.
# Design 10799: 1 resolution(s), autom. group order 5760, decomposable
D[10799]:=[[1,2,3,4],[1,2,3,4],[1,5,6,7],[1,5,6,7],
[1,8,9,10],[1,8,9,10],[1,11,12,13],[1,11,12,13],
[1,14,15,16],[1,14,15,16],[2,5,8,11],[2,5,8,11],
[2,6,12,14],[2,6,12,14],[2,7,9,15],[2,7,9,15],
[2,10,13,16],[2,10,13,16],[3,5,13,15],[3,5,13,15],
[3,6,8,16],[3,6,8,16],[3,7,10,12],[3,7,10,12],
[3,9,11,14],[3,9,11,14],[4,5,10,14],[4,5,10,14],
[4,6,9,13],[4,6,9,13],[4,7,11,16],[4,7,11,16],
[4,8,12,15],[4,8,12,15],[5,9,12,16],[5,9,12,16],
[6,10,11,15],[6,10,11,15],[7,8,13,14],[7,8,13,14]];
G[10799]:=Group([(5,6,7)(8,12,15)(9,11,14)(10,13,16),
(5,8,11)(6,9,13)(7,10,12)(14,15,16),
(3,4)(6,7)(8,11)(9,12)(10,13)(14,15),
(2,3)(6,7)(8,15)(9,16)(10,14)(11,13),
(2,5)(3,6)(4,7)(9,10)(12,13)(14,15),
(1,2)(6,8)(7,11)(9,12)(10,14)(13,15)]);
R[10799]:=[];
RG[10799]:=[];
# Design 10799 / Resolution 1: autom. group order 5760, decomposable
R[10799][1]:=[[1,35,37,39],[2,36,38,40],[3,17,25,33],
[4,18,26,34],[5,13,19,31],[6,14,20,32],
[7,15,21,27],[8,16,22,28],[9,11,23,29],
[10,12,24,30]];
RG[10799][1]:=Group([(5,16)(6,15)(7,14)(8,13)(9,12)(10,11),
(5,9)(6,10)(7,8)(11,15)(12,16)(13,14),
(5,7,6)(8,15,12)(9,14,11)(10,16,13),
(3,4)(6,7)(8,11)(9,12)(10,13)(14,15),
(2,3)(6,7)(8,15)(9,16)(10,14)(11,13),
(2,5)(3,7)(4,6)(8,11)(9,13)(10,12),
(1,2)(6,8)(7,11)(9,12)(10,14)(13,15)]);
This resolvable 2-(16,4,2) design has automorphism group order 5760 and a unique resolution.
D[10799]:=[[1,2,3,4],[1,2,3,4],[1,5,6,7],[1,5,6,7],
[1,8,9,10],[1,8,9,10],[1,11,12,13],[1,11,12,13],
[1,14,15,16],[1,14,15,16],[2,5,8,11],[2,5,8,11],
[2,6,12,14],[2,6,12,14],[2,7,9,15],[2,7,9,15],
[2,10,13,16],[2,10,13,16],[3,5,13,15],[3,5,13,15],
[3,6,8,16],[3,6,8,16],[3,7,10,12],[3,7,10,12],
[3,9,11,14],[3,9,11,14],[4,5,10,14],[4,5,10,14],
[4,6,9,13],[4,6,9,13],[4,7,11,16],[4,7,11,16],
[4,8,12,15],[4,8,12,15],[5,9,12,16],[5,9,12,16],
[6,10,11,15],[6,10,11,15],[7,8,13,14],[7,8,13,14]];
(Note that there are repeated blocks.)
G[10799]:=Group([(5,6,7)(8,12,15)(9,11,14)(10,13,16),
(5,8,11)(6,9,13)(7,10,12)(14,15,16),
(3,4)(6,7)(8,11)(9,12)(10,13)(14,15),
(2,3)(6,7)(8,15)(9,16)(10,14)(11,13),
(2,5)(3,6)(4,7)(9,10)(12,13)(14,15),
(1,2)(6,8)(7,11)(9,12)(10,14)(13,15)]);
The generator sets given for the automorphism groups are in
general not minimal.
R[10799][1]:=[[1,35,37,39],[2,36,38,40],[3,17,25,33],
[4,18,26,34],[5,13,19,31],[6,14,20,32],
[7,15,21,27],[8,16,22,28],[9,11,23,29],
[10,12,24,30]];
RG[10799][1]:=Group([(5,16)(6,15)(7,14)(8,13)(9,12)(10,11),
(5,9)(6,10)(7,8)(11,15)(12,16)(13,14),
(5,7,6)(8,15,12)(9,14,11)(10,16,13),
(3,4)(6,7)(8,11)(9,12)(10,13)(14,15),
(2,3)(6,7)(8,15)(9,16)(10,14)(11,13),
(2,5)(3,7)(4,6)(8,11)(9,13)(10,12),
(1,2)(6,8)(7,11)(9,12)(10,14)(13,15)]);
says that the first parallel class of the first resolution consists
of blocks 1, 35, 37, 39;
the second parallel class of consists of blocks
2, 36, 38, 40, and so on.
(Blocks are numbered in the order they are listed starting from 1.)
So, R[10799][1] encodes the following resolution:
(Note that there are repeated parallel classes.)[ [ 1, 2, 3, 4 ], [ 5, 9, 12, 16 ], [ 6, 10, 11, 15 ], [ 7, 8, 13, 14 ] ], [ [ 1, 2, 3, 4 ], [ 5, 9, 12, 16 ], [ 6, 10, 11, 15 ], [ 7, 8, 13, 14 ] ], [ [ 1, 5, 6, 7 ], [ 2, 10, 13, 16 ], [ 3, 9, 11, 14 ], [ 4, 8, 12, 15 ] ], [ [ 1, 5, 6, 7 ], [ 2, 10, 13, 16 ], [ 3, 9, 11, 14 ], [ 4, 8, 12, 15 ] ], [ [ 1, 8, 9, 10 ], [ 2, 6, 12, 14 ], [ 3, 5, 13, 15 ], [ 4, 7, 11, 16 ] ], [ [ 1, 8, 9, 10 ], [ 2, 6, 12, 14 ], [ 3, 5, 13, 15 ], [ 4, 7, 11, 16 ] ], [ [ 1, 11, 12, 13 ], [ 2, 7, 9, 15 ], [ 3, 6, 8, 16 ], [ 4, 5, 10, 14 ] ], [ [ 1, 11, 12, 13 ], [ 2, 7, 9, 15 ], [ 3, 6, 8, 16 ], [ 4, 5, 10, 14 ] ], [ [ 1, 14, 15, 16 ], [ 2, 5, 8, 11 ], [ 3, 7, 10, 12 ], [ 4, 6, 9, 13 ] ], [ [ 1, 14, 15, 16 ], [ 2, 5, 8, 11 ], [ 3, 7, 10, 12 ], [ 4, 6, 9, 13 ] ]
Below is an example of a 2-(13,6,5) design.
# Design 9450: autom. group order 156, simple, derived
B[9450]:=[[1,2,3,4,5,6],[1,2,3,7,8,9],[1,2,4,7,10,11],[1,2,5,8,10,12],
[1,2,9,11,12,13],[1,3,4,7,12,13],[1,3,5,10,11,13],[1,3,6,9,10,12],
[1,4,5,8,9,11],[1,4,6,8,10,13],[1,5,6,7,9,13],[1,6,7,8,11,12],
[2,3,4,9,10,13],[2,3,5,7,11,12],[2,3,6,8,11,13],[2,4,5,7,8,13],
[2,4,6,8,9,12],[2,5,6,9,10,11],[2,6,7,10,12,13],[3,4,6,7,9,11],
[3,4,8,10,11,12],[3,5,6,7,8,10],[3,5,8,9,12,13],[4,5,6,11,12,13],
[4,5,7,9,10,12],[7,8,9,10,11,13]];
G[9450]:=Group([(2,3)(4,7)(5,9)(6,8)(10,12)(11,13),
(2,4,3,7)(5,13,9,11)(6,12,8,10),
(2,5,6,7,11,10,3,9,8,4,13,12),
(1,2)(3,9)(4,12)(5,11)(6,13)(7,8)]);