On the size of Kakeya sets in finite fields

Abstract

A Kakeya set is a subset of F^n, where 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 * q^n, where C_n depends only on n. This improves the previously best lower bound for general n of ~q^{4n/7}.

Improved bound and added references

References in corpus (1)

• From rotating needles to stability of waves; emerging connections between combinatorics, analysis and PDE

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