The non-existence of certain large minimal blocking sets

Abstract

Recently, Blokhuis and Metsch [6] proved that a Desarguesian projective plane of square order q ≥ 25 contains no minimal blocking -set. Since for q = 4 the existence is proved in [2], the problem is open when q ∈ {9, 16}, see also [4]. In this paper we prove the theorem for q = 9. Since the techniques are of combinational type, based on incidence properties, the result holds also in non-Desarguesian cases. The length of the proof shows the difficulty to treat this subject in a general finite projective plane.