Steiner Triple Systems of Order 21 with a Transversal Subdesign TD(3, 6) View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2020-01

AUTHORS

Y. Guan, M. J. Shi, D. S. Krotov

ABSTRACT

A Steiner triple system (STS) contains a transversal subdesign TD(3, w) if its point set has three pairwise disjoint subsets A, B, C of size w and w2 blocks of the STS intersect with each of A, B, C (those w2 blocks form a TD(3,w)). We prove several structural properties of Steiner triple systems of order 3w + 3 that contain one or more transversal subdesigns TD(3, w). Using exhaustive search, we find that there are 2 004 720 isomorphism classes of STS(21) containing a subdesign TD(3, 6) (or, equivalently, a 6 × 6 Latin square). More... »

PAGES

23-32

References to SciGraph publications

  • 1974-12. Nonisomorphic 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
  • 2018-06-15. The classification of Steiner triple systems on 27 points with 3-rank 24 in DESIGNS, CODES AND CRYPTOGRAPHY
  • Identifiers

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    http://scigraph.springernature.com/pub.10.1134/s0032946020010032

    DOI

    http://dx.doi.org/10.1134/s0032946020010032

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