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arXiv · 2209.10045

New Lower Bounds for Cap Sets

Fred Tyrrell
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Abstract

A cap set is a subset of $\mathbb{F}_3^n$ with no solutions to $x+y+z=0$ other than when $x=y=z$. In this paper, we provide a new lower bound on the size of a maximal cap set. Building on a construction of Edel, we use improved computational methods and new theoretical ideas to show that, for large enough $n$, there is always a cap set in $\mathbb{F}_3^n$ of size at least $2.218^n$.

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BibTeXRIS

Fred Tyrrell. 2023-12-12. New Lower Bounds for Cap Sets. https://doi.org/10.19086/da.91076

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