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


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Article Info

DATE

2019-04

AUTHORS

Dieter Jungnickel, Spyros S. Magliveras, Vladimir D. Tonchev, Alfred Wassermann

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). More... »

PAGES

831-839

References to SciGraph publications

  • 2017. On Classifying Steiner Triple Systems by Their 3-Rank in MATHEMATICAL ASPECTS OF COMPUTER AND INFORMATION SCIENCES
  • 1978-10. Ranks of incidence matrices of Steiner triple systems in MATHEMATISCHE ZEITSCHRIFT
  • 2006-08. There are 1239 Steiner Triple Systems STS(31) of 2-rank 27 in DESIGNS, CODES AND CRYPTOGRAPHY
  • 2018-03. On Bonisoli’s theorem and the block codes of Steiner triple systems in DESIGNS, CODES AND CRYPTOGRAPHY
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1007/s10623-018-0502-5

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    http://dx.doi.org/10.1007/s10623-018-0502-5

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