Algebraic capsets
Abstract
Capsets are subsets of $\mathbb{F}_3^n$ with no three points on a line and a capset is complete if it is not a subset of a larger capset. We study some new constructions of capsets via algebraic equations over extensions of $\mathbb{F}_3$. In particular we construct the smallest known complete capsets with size proportional to the best known lower bound.
Fields of Study & Subjects
Limits and Structures in Graph Theory
Advanced Combinatorial Mathematics
Coding theory and cryptography
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 5 February 2026
- Document type
- Preprint