English

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}.

Keywords

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