Abstract

Marcugini et al. proved, by computer-based proof, the unicity of the maximum (k,3)-arc in PG(2,7). In this paper, we show how the (15,3)-Arc in PG(2,7) may be described using only geometrical properties. The description we provide, believing it is novel, relies on the union of a conic and a complete external quadrangle.

Highlights

  • The main contribution of this paper is the geometric construction of the (15,3)-Arc in PG(2,7), relying on the union of a conic and a complete external quadrangle

  • The construction has a large automorphism group and a nice structure. This is in line with normal experience in all branches of finite geometry

  • All authors have read and agreed to the published version of the manuscript

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Summary

Introduction

Let x and y denote the number of outer points of type (0,4,1,3) and (2,1,1,4), respectively, of a 2−line l2 .

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