There exist Steiner systems $S(2,7,505)$, $S(2,7,589)$, and $S(2,8,624)$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908959457148928 |
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| author | Hetman, Ivan |
| author_facet | Hetman, Ivan |
| contents | In this note two Steiner systems $S(2,7,505)$, two Steiner systems $S(2,7,589)$, and ten Steiner systems $S(2,8,624)$ are presented. This resolves two of $21$ undecided cases for block designs with block length $7$, and one of $37$ cases for block designs with block length $8$, mentioned in Handbook of Combinatorial Designs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04975 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | There exist Steiner systems $S(2,7,505)$, $S(2,7,589)$, and $S(2,8,624)$ Hetman, Ivan Combinatorics 51E05, 51E10 In this note two Steiner systems $S(2,7,505)$, two Steiner systems $S(2,7,589)$, and ten Steiner systems $S(2,8,624)$ are presented. This resolves two of $21$ undecided cases for block designs with block length $7$, and one of $37$ cases for block designs with block length $8$, mentioned in Handbook of Combinatorial Designs. |
| title | There exist Steiner systems $S(2,7,505)$, $S(2,7,589)$, and $S(2,8,624)$ |
| topic | Combinatorics 51E05, 51E10 |
| url | https://arxiv.org/abs/2604.04975 |