The classification of Steiner triple systems on 27 points with 3-rank 24

Authors

Dieter Jungnickel, University of Augsburg
Spyros Magliveras, Florida Atlantic University
Vladimir Tonchev, Michigan Technological UniversityFollow
Alfred Wassermann, University of Bayreuth

Document Type

Article

Publication Date

4-2019

Abstract

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).

Publisher's Statement

© Springer Science+Business Media, LLC, part of Springer Nature 2018. Publisher’s version of record: https://doi.org/10.1007/s10623-018-0502-5

Publication Title

Designs, Codes and Cryptography

Recommended Citation

Jungnickel, D., Magliveras, S., Tonchev, V., & Wassermann, A. (2019). The classification of Steiner triple systems on 27 points with 3-rank 24. Designs, Codes and Cryptography, 87(4), 831-839. http://doi.org/10.1007/s10623-018-0502-5
Retrieved from: https://digitalcommons.mtu.edu/math-fp/69