On the size of Kakeya sets in finite fields

Dvir, Zeev

doi:10.1090/S0894-0347-08-00607-3

On the size of Kakeya sets in finite fields
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by Zeev Dvir

J. Amer. Math. Soc. 22 (2009), 1093-1097

DOI: https://doi.org/10.1090/S0894-0347-08-00607-3

Published electronically: June 23, 2008

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Abstract:

A Kakeya set is a subset of $\mathbb {F}^n$, where $\mathbb {F}$ is a finite field of $q$ elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least $C_{n} \cdot q^{n}$, where $C_{n}$ depends only on $n$. This answers a question of Wolff.

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