Classification of Resolvable 2-(14,7,12) and 3-(14,7,5) Designs

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.

The resolvable 2-(14,7,12) and 3-(14,7,5) designs

|Aut(D)|Resolvable designs
11 360 800
21 819
3748
463
637
81
1213
131
241
392
1561
Total1 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].


File format

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)]);

Petteri Kaski (Petteri.Kaski@hut.fi)