A new lower bound for the size of an affine blocking set

Abstract

A blocking set in an affine plane is a set of points $B$ such that every line contains at least one point of $B$. The best known lower bound for blocking sets in arbitrary (non-desarguesian) affine planes was derived in the 1980's by Bruen and Silverman. In this note, we improve on this result by showing that a blocking set of an affine plane of order $q$, $q\ge 25$, contains at least $q+\lfloor \sqrt{q}\rfloor +3$ points.