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arXiv · 2602.05254

Algebraic capsets

Cassie Grace·José Felipe Voloch
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Abstract

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.

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Cassie Grace, José Felipe Voloch. 2026-03-09. Algebraic capsets. https://arxiv.org/abs/2602.05254

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