Large blocking sets in PG(2,q2)

Abstract

Minimal blocking sets in PG(2,q2) have size at most q3+1. This result is due to Bruen and Thas and the bound is sharp, sets attaining this bound are called unitals. In this paper, we show that the second largest minimal blocking sets have size at most q3+1−(p−3)/2, if q=p, p≥67, or q=ph, p>7, h>1. Our proof also works for sets having at least one tangent at each of its points (that is, for tangency sets).