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

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 for q square. We can also prove a similar result for certain values of the intervals and .