@article{
    Kaski05,
    author = "Kaski, Petteri",
    note = "",
    title = "Isomorph-free exhaustive generation of designs with prescribed groups of automorphisms",
    url = "http://dx.doi.org/10.1137/S0895480104444788",
    journal = "SIAM Journal on Discrete Mathematics",
    number = "3",
    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.",
    month = "",
    volume = "19",
    year = "2005",
    keywords = "classification algorithm, combinatorial search, consistency checking, isomorph rejection, isomorph-free generation, Kramer-Mesner method, Steiner triple system, symmetry reduction",
    pages = "664--690"
}