On multiple blocking sets in Galois planes

This article continues the study of multiple blocking sets in PG(2, q). In [3], using lacunary polynomials, it was proven that t-fold blocking sets of PG(2, q), q square, t < q1/4/2, of size smaller than t(q + 1) + cqq 2/3, with cq = 2 −1/3 when q is a power of 2 or 3 and cq = 1 otherwise, contain the union of t pairwise disjoint Baer subplanes when t ≥ 2, or a line or a Baer subplane when t = 1. We now combine the method of lacunary polynomials with the use of algebraic curves to improve the known characterization results on multiple blocking sets and to prove a t (mod p) result on small t-fold blocking sets of PG(2, q = pn), p prime, n ≥ 1.