Arcs, blocking sets, and minihypers

A (k, n)-arc in a finite projective plane IIq of order q is a set of k poin ts with some n but no n + 1 collinear points where k > n and 2 less than or equal to n less than or equal to q. The maximum value of k for which a (k, n)-arc exists in PG(2, q) is denoted by m(n)(2, q). It is well known that if n is not a divisor of q, then m(n)(2, q) less than or equal to (n - 1)q + n - 3. The purpose of this paper is to improve this upper bound on m(n) ( 2, q) using the nonexistence of some minihypers in PG(2, q) and to characte rize some minihypers in PG(t, q) where t greater than or equal to 3. (C) 20 00 Elsevier Science Ltd. All rights reserved.