Finite field Nikodym problem for spread line sets
Abstract
A set of points $N\subseteq \mathbb{F}_q^d$ is a Nikodym set if, for any $x\in \mathbb{F}_q^d$, there is a line $\ell$ through $x$ such that $\ell\setminus\{x\}\subseteq N$. We conjecture that $|N|=q^d-O_d(q^{d/(d-1)})$ and prove it under an extra algebraic assumption.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Combinatorial Mathematics
Analytic Number Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 January 2026
- Document type
- Preprint