New lower bounds on the size of (n,r)-arcs in PG(2,q)

2018/08/08 by Braun, Michael
#05B25 #51E21 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.02702

Abstract

An (n,r)-arc in PG(2,q) is a set of n points such that each line contains at most r of the selected points. It is well-known that (n,r)-arcs in PG(2,q) correspond to projective linear codes. Let m_r(2,q) denote the maximal number n of points for which an (n,r)-arc in PG(2,q) exists. In this paper we obtain improved lower bounds on m_r(2,q) by explicitly constructing (n,r)-arcs. Some of the constructed (n,r)-arcs correspond to linear codes meeting the Griesmer bound. All results are obtained by integer linear programming.

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