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 . We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines in , 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}
}