Small stopping sets in finite projective planes of order q

A configuration C in a (finite) incidence structure is a subset C of blocks. If every point on a block of C belongs to at least one other block of C, then C is called stopping set (or equivalently full configuration). If s_min(q) is the minimal size of a stopping set in a finite projective plane of odd order q, then either s_min(q) is greater than or equal to q+5 if 3 does not divide q or s_min(q) greater than or equal to q+3 if 3 divides q. In this note, we prove that s_min(q) greater than or equal to q + 5 for any odd q different form 3. If q = 3, then s_min(3) = 6 and a stopping set of minimal size 6 in PG(2; 3) is the dual set of the symmetric difference of two lines. Also, we study stopping sets of size q+4 in a finite projective plane of order q.