On blocking sets in affine planes

Denote by _q an affine plane of order q. In the desarguesian case _q=AG(2,q), q 5(q= p^h, p prime), we prove that the smallest cardinality of a blocking set is 2q–1. In any arbitrary affine plane _q (desarguesian or not) with q5, for any integer k with 2q–1 k(q–1)², we construct a blocking set S with ¦S¦=k. For an irreducible blocking set S of _q we determine the upper bound S qq]+1. We prove that if _q contains a blocking set S which is irreducible with its complementary blocking set, then necessarily _q=AG(2, 4) and S is uniquely determined. Finally we introduce techniques to obtain blocking sets in AG(2, q) and in PG(2, q).Research partially supported by G.N.S.A.G.A. (CNR)