English

Finite field Kakeya and Nikodym sets in three dimensions

Combinatorics 2019-03-06 v3

Abstract

We give improved lower bounds on the size of Kakeya and Nikodym sets over Fq3\mathbb{F}_q^3. We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines in Fq3\mathbb{F}_q^3, and show that this conjecture implies an optimal bound on the size of a Nikodym set.

Keywords

Cite

@article{arxiv.1609.01048,
  title  = {Finite field Kakeya and Nikodym sets in three dimensions},
  author = {Ben Lund and Shubhangi Saraf and Charles Wolf},
  journal= {arXiv preprint arXiv:1609.01048},
  year   = {2019}
}
R2 v1 2026-06-22T15:39:49.302Z