Details

Autor(en) / Beteiligte

• Szőnyi, Tamás

Titel

Blocking Sets in Desarguesian Affine and Projective Planes

Ist Teil von

• Finite fields and their applications, 1997-07, Vol.3 (3), p.187-202

Ort / Verlag

Elsevier Inc

Erscheinungsjahr

1997

Quelle

Elsevier Journal Backfiles on ScienceDirect (DFG Nationallizenzen)

Beschreibungen/Notizen

• In this paper we show that blocking sets of cardinality less than 3(q+ 1)/2 (q=pn) in Desarguesian projective planes intersect every line in 1 moduloppoints. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous results of Rédei, which were proved for a special class of blocking sets. In the particular caseq=p2, the above result implies that a nontrivial blocking set either contains a Baer-subplane or has size at least 3(q+ 1)/2; and this result is sharp. As a by-product, new proofs are given for the Jamison, Brouwer-Schrijver theorem on blocking sets in Desarguesian affine planes, and for Blokhuis' theorem on blocking sets in Desarguesian projective planes.