Generalized hyperfocused arcs in PG(2,p)

A generalized hyperfocused arc H in PG(2,q) is an arc of size k with the property that the k(k-1)/2 secants can be blocked by a set of k-1 points not belonging to the arc. We show that if q is a prime and H is a generalized hyperfocused arc of size k, then k=1, 2 or 4. Interestingly, this problem is also related to the (strong) cylinder conjecture ( Problem 919), as we point out in the last section. Keywords: hyperfocused arc; dual 3-net