Reference:
Petteri Kaski and Patric R. J. Östergård. The Steiner triple systems of order 19. Mathematics of Computation, 73:2075–2092, 2004.
Abstract:
Using an orderly algorithm, the Steiner triple systems of order are classified; there are pairwise nonisomorphic such designs. For each design, the order of its automorphism group and the number of Pasch configurations it contains are recorded; of the designs are antiPasch. There are three main parts of the classification: constructing an initial set of blocks, the seeds; completing the seeds to triple systems with an algorithm for exact cover; and carrying out isomorph rejection of the final triple systems. Isomorph rejection is based on the graph canonical labeling software emphnauty supplemented with a vertex invariant based on Pasch configurations. The possibility of using the (strongly regular) block graphs of these designs in the isomorphism tests is utilized. The aforementioned value is in fact a lower bound on the number of pairwise nonisomorphic strongly regular graphs with parameters .
Keywords:
automorphism group, orderly algorithm, Pasch configuration, Steiner triple system
Suggested BibTeX entry:
@article{KaOs04c,
author = {Petteri Kaski and Patric R. J. {\"O}sterg{\aa}rd},
journal = {Mathematics of Computation},
pages = {20752092},
title = {The {S}teiner triple systems of order 19},
volume = {73},
year = {2004},
}
