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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.13331 |
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| _version_ | 1866908707751723008 |
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| author | Hanaki, Akihide Kobayashi, Kenji Munemasa, Akihiro |
| author_facet | Hanaki, Akihide Kobayashi, Kenji Munemasa, Akihiro |
| contents | We consider when the projective special linear group over a finite field defines a $3$-design with a cyclic starter block. We will show that the equivalences of the existence of such $3$-$(q+1,5,3)$ and $3$-$(q+1,10,18)$ designs for a prime power $q\equiv 1\pmod{20}$, and $3$-$(q+1,13,33)$ and $3$-$(q+1,26,150)$ designs for a prime power $q\equiv 1\pmod{52}$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13331 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 3-Designs from PSL(2,q) with cyclic starter blocks Hanaki, Akihide Kobayashi, Kenji Munemasa, Akihiro Combinatorics Group Theory 05B05 We consider when the projective special linear group over a finite field defines a $3$-design with a cyclic starter block. We will show that the equivalences of the existence of such $3$-$(q+1,5,3)$ and $3$-$(q+1,10,18)$ designs for a prime power $q\equiv 1\pmod{20}$, and $3$-$(q+1,13,33)$ and $3$-$(q+1,26,150)$ designs for a prime power $q\equiv 1\pmod{52}$, respectively. |
| title | 3-Designs from PSL(2,q) with cyclic starter blocks |
| topic | Combinatorics Group Theory 05B05 |
| url | https://arxiv.org/abs/2502.13331 |