New (n, r)-arcs in PG(2, 17), PG(2, 19), and PG(2, 23)

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 m r (2, q). In this paper a new (95, 7)-arc, (183, 12)-arc, and (205, 13)-arc in PG(2, 17) are constructed, as well as a (243, 14)-arc and (264, 15)-arc in PG(2, 19). Likewise, good large (n, r)-arcs in PG(2, 23) are constructed and a table with bounds on m r (2, 23) is presented. In this way many new 3-dimensional Griesmer codes are obtained. The results are obtained by nonexhaustive local computer search.