@article{
    KaOs04c,
    author = {Kaski, Petteri and {\"O}sterg{\aa}rd, Patric R. J.},
    title = "The {S}teiner triple systems of order 19",
    url = "http://www.ams.org/mcom/2004-73-248/S0025-5718-04-01626-6/",
    journal = "Mathematics of Computation",
    abstract = "Using an orderly algorithm, the Steiner triple systems of order $19$ are classified; there are $11,\!084,\!874,\!829$ pairwise nonisomorphic such designs. For each design, the order of its automorphism group and the number of Pasch configurations it contains are recorded; $2,\!591$ of the designs are anti-Pasch. 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 \emph{nauty} 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 $(57,24,11,9)$.",
    volume = "73",
    year = "2004",
    keywords = "automorphism group, orderly algorithm, Pasch configuration, Steiner triple system",
    pages = "2075--2092"
}