Note on disjoint blocking sets in Galois planes

A blocking set in a projective or affine plane is a set of points, which intersects every line. Blocking sets are particular cases of 1-covers in hypergraphs. For projective planes, the smallest blocking sets are just the lines. Blocking sets containing a line will be called trivial. A blocking set is said to be minimal (or irreducible) when no proper subset of it is a blocking set. In this paper, we show that there are at least cq disjoint blocking sets in PG(2; q), where c is about 1/3. The result also extends to some non-Desarguesian planes of order q.