Mathematics > Combinatorics
[Submitted on 20 Sep 2022 (v1), last revised 12 Dec 2023 (this version, v2)]
Title:New Lower Bounds for Cap Sets
View PDF HTML (experimental)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 $2.218^n$.
Submission history
From: Fred Tyrrell [view email][v1] Tue, 20 Sep 2022 23:44:52 UTC (24 KB)
[v2] Tue, 12 Dec 2023 14:46:04 UTC (39 KB)
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