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<p>In this article, we construct a Steiner system with the parameters <i>S</i>(3,&#xa0;6,&#xa0;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.</p>

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Steiner 3-designs as extensions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月7日

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  • Michael Kiermaier,
  • Vedran Krčadinac,
  • Alfred Wassermann

摘要

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.