New lower bounds for cap sets

09/20/2022

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by   Fred Tyrrell, et al.

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A cap set is a subset of 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 𝔽_3^n of size at least 2.218^n.