Steiner triple systems of order 19 with nontrivial automorphism group

Abstract

There are 172,248 Steiner triple systems of order 19 having a nontrivial automorphism group. Computational methods suitable for generating these designs are developed. The use of tactical configurations in conjunction with orderly algorithms underlies practical techniques for the generation of the designs, and the subexponential time isomorphism technique for triple systems is improved in practice to test isomorphisms of the designs. The automorphism group of each of the triple systems is computed, and a summary presented of the number of systems with each possible type of automorphism.