Abstract
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.
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