On the cardinality of blocking sets in PG(2,q)

Abstract

Denote by PG(2,q) the finite desarguesian projective plane of order q, where q=ph, p a prime, q>2. We define the function m(q) as follows: m(q)=√q, if q is a square; m(q)=(q+1)/2, if q is a prime; m(q)=ph−d, if q=ph with h an odd integer, where d denotes the greatest divisor of h different from h. The following theorem is proved: For any integer k with q+m(q)+1 ⩽ k ⩽ q2−m(q), there exists a blocking set in PG(2,q) having exactly k elements.