Recently, Blokhuis and Metsch proved that a Desarguesian projective plane of square order q^2>=25 contains no minimal blocking q^3-set. Since for q=4 the existence is proved, the problem is open when q^2 =9, 16. In this paper we prove the theorem for q=9. Since the techniques are of combinatorial type, based on incidence properties, the result holds also in non-Desarguesian cases. The lenght of the proof shows the difficulty to treat this subject in a general finite projective plane.
The non-existence of certain large minimal blocking sets
INNAMORATI, STEFANO
1998-01-01
Abstract
Recently, Blokhuis and Metsch proved that a Desarguesian projective plane of square order q^2>=25 contains no minimal blocking q^3-set. Since for q=4 the existence is proved, the problem is open when q^2 =9, 16. In this paper we prove the theorem for q=9. Since the techniques are of combinatorial type, based on incidence properties, the result holds also in non-Desarguesian cases. The lenght of the proof shows the difficulty to treat this subject in a general finite projective plane.File in questo prodotto:
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