The classification of Steiner triple systems on 27 points with 3-rank 24
We show that there are exactly 2624 isomorphism classes of Steiner triple systems on 27 points having 3-rank 24, all of which are actually resolvable. More generally, all Steiner triple systems on 3n points having 3-rank at most 3n−n are resolvable. Combining this observation with the lower bound on the number of such STS(3n) recently established by two of the present authors, we obtain a strong lower bound on the number of Kirkman triple systems on 3n points. For instance, there are more than 1099 isomorphism classes of KTS(81).
Designs, Codes and Cryptography
The classification of Steiner triple systems on 27 points with 3-rank 24.
Designs, Codes and Cryptography,
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© Springer Science+Business Media, LLC, part of Springer Nature 2018. Publisher’s version of record: https://doi.org/10.1007/s10623-018-0502-5