On the number of pairwise non-isomorphic minimal blocking sets in PG(2, q)

Abstract

In this paper we examine whether the number of pairwise non-isomorphic minimal blocking sets in PG(2, q) of a certain size is larger than polynomial. Our main result is that there are more than polynomial pairwise non-isomorphic minimal blocking sets for any size in the intervals [2q−1, 3q−4] for q odd and $[5q\log q,q\sqrt q-2q]$ for q square. We can also prove a similar result for certain values of the intervals $[cq\log q,Cq\log q], [\frac{3}{2}q,2q]$ and $[q\sqrt q-2q,q\sqrt q+1]$ .