On the size of Kakeya sets in finite vector spaces

TL;DR

This paper investigates the minimal size of Kakeya sets in finite vector spaces over GF(q), especially focusing on new upper bounds when q is even, contributing to the understanding of geometric configurations in finite fields.

Contribution

It provides novel upper bounds on the size of Kakeya sets in GF(q)^n for even q, advancing theoretical knowledge in finite geometry.

Findings

Derived new upper bounds for Kakeya sets when q is even

Improved understanding of geometric configurations in finite fields

Contributed to finite field combinatorics and geometry

Abstract

For a finite field GF(q) a Kakeya set K is a subset of GF(q)^n that contains a line in every direction. This paper derives new upper bounds on the minimum size of Kakeya sets when q is even.