Steiner 3-designs as extensions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908562881511424 |
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| author | Kiermaier, Michael Krčadinac, Vedran Wassermann, Alfred |
| author_facet | Kiermaier, Michael Krčadinac, Vedran Wassermann, Alfred |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23483 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Steiner 3-designs as extensions Kiermaier, Michael Krčadinac, Vedran Wassermann, Alfred Combinatorics 05B05 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. |
| title | Steiner 3-designs as extensions |
| topic | Combinatorics 05B05 |
| url | https://arxiv.org/abs/2509.23483 |