Sharp density bounds on the finite field Kakeya problem

Abstract

A Kakeya set in ${\mathbb{F}}_q^n$ is a set containing a line in every direction. We show that every Kakeya set in ${\mathbb{F}}_q^n$ has density at least $1/2^{n-1}$, matching the construction by Dvir, Kopparty, Saraf and Sudan.

9 pages, 1 figure

References in corpus (2)

• Improved lower bound on the size of Kakeya sets over finite fields
• Finite field Kakeya and Nikodym sets in three dimensions