Arcs, blocking sets, and minihypers

A (k, n)-arc in a finite projective plane Пq of order q is a set of k points with some n but no n + 1 collinear points where k> n and 2 ≤ n ≤ q. The maximum value of k for which a (k, n)-arc exists in PG(2, q) is denoted by mn(2, q). It is well known that if n is not a divisor of q, then mn(2, q) ≤ (n − 1)q + n − 3. The purpose of this paper is to improve this upper bound on mn(2, q) using the nonexistence of some minihypers in PG(2, q) and to characterize some minihypers in PG(t, q) where t ≥ 3.