Proof of a conjecture of Metsch

In this paper we prove a conjecture of Metsch about the maximum number of lines intersecting a pointset in PG ( 2 , q ) , presented at the conference “Combinatorics 2002”. As a consequence, we give a short proof of the famous Jamison, Brouwer and Schrijver bound on the size of the smallest affine blocking set in AG ( 2 , q ) .