Improved Bounds onmr(2,q) q=19,25,27

摘要

An (n,r)-arc is a set ofnpoints of a projective plane such that somer, but nor+1of them, are collinear. The maximum size of an (n,r)-arc in PG(2,q) is denoted bymr(2,q). In this paper, a new (286, 16)-arc in PG(2,19), a new (341, 15)-arc, and a (388, 17)-arc in PG(2,25) are constructed, as well as a (394, 16)-arc, a (501, 20)-arc, and a (532, 21)-arc in PG(2,27). Tables with lower and upper bounds onmr(2, 25) andmr(2, 27) are presented as well. The results are obtained by nonexhaustive local computer search.