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Abstract <p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(AG\left( {16,3} \right)\)</EquationSource> <!--PatRec2570068Karapetyana-m1--> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(AG\left( {21,3} \right)\)</EquationSource> <!--PatRec2570068Karapetyana-m2--> </InlineEquation>, and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(AG\left( {22,3} \right)\)</EquationSource> <!--PatRec2570068Karapetyana-m3--> </InlineEquation>, respectively.</p>

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On Some Large Cap Sets

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Iskandar Karapetyan,
  • Karen Karapetyan

摘要

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 \(AG\left( {16,3} \right)\) , \(AG\left( {21,3} \right)\) , and \(AG\left( {22,3} \right)\) , respectively.