Finite field Kakeya and Nikodym sets in three dimensions

Abstract

We give improved lower bounds on the size of Kakeya and Nikodym sets over ${\mathbb{F}}_q^3$. We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines in ${\mathbb{F}}_q^3$, and show that this conjecture implies an optimal bound on the size of a Nikodym set.

References in corpus (1)

• Incidence Bounds for Block Designs

Cited by in corpus (1)

• Sharp density bounds on the finite field Kakeya problem