This is the webpage of the paper ``Classification of Resolvable 2-(14,7,12) and 3-(14,7,5) Designs'' by P. Kaski, L. B. Morales, P. R. J. Östergård, D. A. Rosenblueth, and C. Velarde (Journal of Combinatorial Mathematics and Combinatorial Computing 47 (2003), 65-74).
The resolvable designs 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 | 1 360 800 |
2 | 1 819 |
3 | 748 |
4 | 63 |
6 | 37 |
8 | 1 |
12 | 13 |
13 | 1 |
24 | 1 |
39 | 2 |
156 | 1 |
Total | 1 363 486 |
The 2 686 resolvable designs with a nontrivial full automorphism group are also available in one gzip-compressed file res14712.txt.gz [258KB].
The data files are presented in ASCII format suitable for the GAP toolkit. For each design we tabulate parallel class by parallel class its unique resolution. This is followed by a set of generator permutations for the full automorphism group of the design.
An example is given below:
# Design 1015: 1 resolution(s), autom. group order 156, simple R[1015]:=[[[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]], [[1,2,3,4,5,6,8],[7,9,10,11,12,13,14]], [[1,2,3,4,9,10,11],[5,6,7,8,12,13,14]], [[1,2,3,5,9,12,13],[4,6,7,8,10,11,14]], [[1,2,3,6,10,12,14],[4,5,7,8,9,11,13]], [[1,2,4,7,8,13,14],[3,5,6,9,10,11,12]], [[1,2,4,7,10,13,14],[3,5,6,8,9,11,12]], [[1,2,5,7,10,11,12],[3,4,6,8,9,13,14]], [[1,2,5,8,9,12,13],[3,4,6,7,10,11,14]], [[1,2,6,8,9,11,14],[3,4,5,7,10,12,13]], [[1,2,6,9,11,13,14],[3,4,5,7,8,10,12]], [[1,2,7,8,10,11,12],[3,4,5,6,9,13,14]], [[1,3,4,7,9,12,14],[2,5,6,8,10,11,13]], [[1,3,4,8,9,10,11],[2,5,6,7,12,13,14]], [[1,3,5,8,10,13,14],[2,4,6,7,9,11,12]], [[1,3,5,10,11,13,14],[2,4,6,7,8,9,12]], [[1,3,6,7,8,11,13],[2,4,5,9,10,12,14]], [[1,3,6,7,11,12,13],[2,4,5,8,9,10,14]], [[1,3,7,8,9,12,14],[2,4,5,6,10,11,13]], [[1,4,5,6,11,12,14],[2,3,7,8,9,10,13]], [[1,4,5,7,9,11,13],[2,3,6,8,10,12,14]], [[1,4,5,8,11,12,14],[2,3,6,7,9,10,13]], [[1,4,6,8,10,12,13],[2,3,5,7,9,11,14]], [[1,4,6,9,10,12,13],[2,3,5,7,8,11,14]], [[1,5,6,7,8,9,10],[2,3,4,11,12,13,14]], [[1,5,6,7,9,10,14],[2,3,4,8,11,12,13]]]; G[1015]:=Group([(2,3,12,6,14,10)(4,9,13,11,5,7), (2,4,3,9,12,13,6,11,14,5,10,7), (1,2)(3,10)(4,12)(5,7)(6,11)(9,14)]);