English

Algebraic capsets

Combinatorics 2026-03-10 v2

Abstract

Capsets are subsets of F3n\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 F3\mathbb{F}_3. In particular we construct the smallest known complete capsets with size proportional to the best known lower bound.

Keywords

Cite

@article{arxiv.2602.05254,
  title  = {Algebraic capsets},
  author = {Cassie Grace and José Felipe Voloch},
  journal= {arXiv preprint arXiv:2602.05254},
  year   = {2026}
}
R2 v1 2026-07-01T09:37:09.411Z