Steiner 3-designs as extensions

Titelangaben

Kiermaier, Michael ; Krčadinac, Vedran ; Wassermann, Alfred:
Steiner 3-designs as extensions.
In: Designs, Codes and Cryptography. Bd. 94 (2026) . - 157.
ISSN 1573-7586
DOI: https://doi.org/10.1007/s10623-026-01888-w

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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.