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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.05254 |
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| _version_ | 1866915844976541696 |
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| author | Grace, Cassie Voloch, José Felipe |
| author_facet | Grace, Cassie Voloch, José Felipe |
| contents | Capsets are subsets of $\mathbb{F}_3^n$ with no three points on a line and a capset is complete if it is not a subset of a larger capset. We study some new constructions of capsets via algebraic equations over extensions of $\mathbb{F}_3$. In particular we construct the smallest known complete capsets with size proportional to the best known lower bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Algebraic capsets Grace, Cassie Voloch, José Felipe Combinatorics Capsets are subsets of $\mathbb{F}_3^n$ with no three points on a line and a capset is complete if it is not a subset of a larger capset. We study some new constructions of capsets via algebraic equations over extensions of $\mathbb{F}_3$. In particular we construct the smallest known complete capsets with size proportional to the best known lower bound. |
| title | Algebraic capsets |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.05254 |