Abstract
Denote byα q an affine plane of order q. In the desarguesian case αq=AG(2,q), q ⩾ 5(q= ph, p prime), we prove that the smallest cardinality of a blocking set is 2q−1. In any arbitrary affine plane αq (desarguesian or not) with q⩾5, for any integer k with 2q−1⩽ k⩽(q−1)2, we construct a blocking set S with ¦S¦=k. For an irreducible blocking set S of αq we determine the upper bound S⩾ [q√q]+1. We prove that if ⇌q contains a blocking set S which is irreducible with its complementary blocking set, then necessarily αq=AG(2, 4) and S is uniquely determined. Finally we introduce techniques to obtain blocking sets in AG(2, q) and in PG(2, q).
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Research partially supported by G.N.S.A.G.A. (CNR)
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Berardi, L., Eugeni, F. On blocking sets in affine planes. J Geom 22, 167–177 (1984). https://doi.org/10.1007/BF01222841
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DOI: https://doi.org/10.1007/BF01222841