Improved explicit upper bounds for the Cap Set Problem

Abstract

Ellenberg and Gijswijt gave the best known asymptotic upper bound for the cardinality of subsets of ${\mathbb{F}}_q^n$ without 3-term arithmetic progressions. We improve this bound by a factor $\sqrt{n}$. In the case $q=3$, we also obtain more explicit upper bounds for the Cap Set Problem.

References in corpus (1)

• Progression-free sets in Z_4^n are exponentially small

Cited by in corpus (1)

• Maximal line-free sets in ${\mathbb{F}}_p^n$