Blocking sets in projective spaces

In this paper we collect results on the possible sizes of k-blocking sets. Since previous surveys focused mainly on blocking sets in the plane, we concentrate our attention on blocking sets in higher dimensions. Lower bounds on the size of the smallest non-trivial k-blocking set are surveyed in detail. The linearity conjecture and known results supporting the conjecture (e.g. proofs in particular cases) are collected. The known constructions are also presented. In case of planar minimal blocking sets we only discuss the constructions briefly. In case of higher dimensions the situation is not satisfactory, there are more open questions than known constructions. Keywords: (Semi-)ovoid; Blocking set; Minihyper; Rédei typ