What does this research mean for the field?

Complete cap sets with sizes 274,432, 13,991,936, and 30,294,016 exist in the affine geometries AG(16,3), AG(21,3), and AG(22,3), respectively. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to construct large complete cap sets in various affine geometries over finite fields.

May 2, 2026

On Some Large Cap Sets

Key Points

This research aims to construct large complete cap sets in various affine geometries over finite fields.
Constructed cap sets in affine geometries AG(16,3), AG(21,3), and AG(22,3).
Focused on achieving specific set sizes of 274,432; 13,991,936; and 30,294,016.
Constructed a complete cap set of size 274,432 in AG(16,3).
Established a complete cap set of size 13,991,936 in AG(21,3).
Created a complete cap set of size 30,294,016 in AG(22,3).

Abstract

A cap set in projective or affine geometry over a finite field is a set of points no three of which are collinear. In this paper we construct complete cap sets with sizes 274 432, 13 991 936, and 30 294 016 in affine geometries AG (16, 3), AG (21, 3), and AG (22, 3), respectively.

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Cite This Study

Karapetyan et al. (Mon,) studied this question.

synapsesocial.com/papers/69f5939871405d493affe9ea https://doi.org/https://doi.org/10.1134/s1054661825700683

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