Proper blocking sets in projective spaces Original Research Article

In this paper we introduce the new concept of proper blocking sets B infinite projective spaces, that means every hyperplane contains a point of B, no line is contained in B, and there is no hyperplane that induces a blocking set. In Theorem 1.4, we prove that a blocking set in PG(d, q), q ⩾ 3, that has less than the number of points of a blocking set in PG(2,q) of minimum cardinality plus one, already contains a blocking set in a plane and is therefore not proper. In the last section, we construct various examples of proper blocking sets with a small number of points.