Steiner 3-designs as extensions

2025/09/27 by Kiermaier, Michael, Krčadinac, Vedran, Wassermann, Alfred
#05B05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.23483

Abstract

In this article, we construct a Steiner system with the parameters S(3,6,42), settling one of the smallest open parameter sets of Steiner 3-designs. Furthermore, we establish the existence of rotational Steiner quadruple systems on 46 and 92 points. Our construction method is based on extending Steiner 2-designs using prescribed extension groups. We also consider extensions to designs of higher strength. The article includes a table and a discussion of the status of all admissible parameters for Steiner 3-designs on at most 50 points.

Citations

• Some new Steiner designs S(2,6,91)
• Higher incidence matrices and tactical decomposition matrices
• The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F
• Practical graph isomorphism, II
• Dancing links

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