# A lower bound for the size of Kakeya sets with respect to hyperplanes in $\mathbb{F}_q^n$

## TL;DR

This paper establishes a lower bound on the size of Kakeya sets in finite fields, showing such sets must be nearly as large as the entire space, with only a small quadratic deficit.

## Contribution

It provides a new lower bound for Kakeya sets with respect to hyperplanes in finite fields, advancing understanding of their minimal size.

## Key findings

- Kakeya sets contain a hyperplane in every direction
- Size of Kakeya sets is at least q^n - O(q^2)
- Sets are nearly as large as the entire space

## Abstract

We prove that a subset of $\mathbb{F}_q^n$ that contains a hyperplane in any direction has size at least $q^{n}-O(q^2)$.