On the size of Kakeya sets in finite fields
Combinatorics
2015-05-13 v3 Classical Analysis and ODEs
Number Theory
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}.
Cite
@article{arxiv.0803.2336,
title = {On the size of Kakeya sets in finite fields},
author = {Zeev Dvir},
journal= {arXiv preprint arXiv:0803.2336},
year = {2015}
}
Comments
Improved bound and added references