Papers › Exponentially Larger Affine and Projective Caps
Exponentially Larger Affine and Projective Caps
Christian Elsholtz, Gabriel F. Lipnik
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
In spite of a recent breakthrough on upper bounds of the size of cap sets (by Croot, Lev and Pach (2017) and Ellenberg and Gijswijt (2017)), the classical cap set constructions had not been affected. In this work, we introduce a very different method of construction for caps in all affine spaces with odd prime modulus p. Moreover, we show that for all primes p ≡5 6 with p ≤41, the new construction leads to an exponentially larger growth of the affine and projective caps in AG(n,p) and PG(n,p). For example, when p=23, the existence of caps with growth (8.0875…)ⁿ follows from a three-dimensional example of Bose (1947), and the only improvement had been to (8.0901…)ⁿ by Edel (2004), based on a six-dimensional example. We improve this lower bound to (9-o(1))ⁿ.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections