Mixed Steiner Triples Systems with Shortest Length
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909748529463296 |
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| author | Etzion, Tuvi |
| author_facet | Etzion, Tuvi |
| contents | We prove that a 3-GDD of type $1^n k^1 \ell^1$, where $n= k \cdot \ell$, with minimum distance 3 exists for every $k$ and $\ell$ such that $n = k \ell$, $k = 1$ or $3~(mod ~ 6)$, and $\ell = 1$ or $3~(mod ~ 6)$. These designs are of the shortest possible length (smallest number of elements) for given $k$ and $\ell$. Other constructions for such triple systems are also presented. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mixed Steiner Triples Systems with Shortest Length Etzion, Tuvi Combinatorics We prove that a 3-GDD of type $1^n k^1 \ell^1$, where $n= k \cdot \ell$, with minimum distance 3 exists for every $k$ and $\ell$ such that $n = k \ell$, $k = 1$ or $3~(mod ~ 6)$, and $\ell = 1$ or $3~(mod ~ 6)$. These designs are of the shortest possible length (smallest number of elements) for given $k$ and $\ell$. Other constructions for such triple systems are also presented. |
| title | Mixed Steiner Triples Systems with Shortest Length |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.12954 |