Abstract
An (n,r)-arc is a set of n points of a projective plane such that some r, but no r+1 of them, are collinear. The maximum size of an (n,r)-arc in PG(2,q) is denoted by mr(2,q). In this paper a (377, 14)-arc, a (514, 18)-arc, a (535, 19)-arc and a (565, 20)-arc in PG(2,31) are presented. The constructed arcs improve the respective lower bounds on mr(2,31) in [Kohnert A., Arcs in the projective planes, Online tables, www.algorithm.uni-bayreuth.de/en/research/Coding_Theory/PG_arc_table/index.html].
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