AUTHORS:
Kaski, Petteri
ABSTRACT:
We develop an algorithm framework for isomorph-free exhaustive generation of designs admitting a group of automorphisms from a prescribed collection of pairwise non-conjugate groups, where each prescribed group has a large index relative to its normalizer in the isomorphism-inducing group. We demonstrate the practicality of the framework by producing a complete classification of the Steiner triple systems of order 21 admitting a nontrivial automorphism group. The number of pairwise nonisomorphic such designs is 62336617, where 958 of the designs are anti-Pasch. We also develop consistency checking methodology for gaining confidence in the correct operation of the algorithm implementation.