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On large minimal blocking sets in PG(2,q)

✍ Scribed by Tamás Szőnyi; Antonello Cossidente; András Gács; Csaba Mengyán; Alessandro Siciliano; Zsuzsa Weiner

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
172 KB
Volume
13
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

The size of large minimal blocking sets is bounded by the Bruen–Thas upper bound. The bound is sharp when q is a square. Here the bound is improved if q is a non‐square. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of non‐prime order. The construction can be regarded as a generalization of Buekenhout's construction of unitals. For example, if q is a cube, then our construction gives minimal blocking sets of size q^4/3^ + 1 or q^4/3^ + 2. Density results for the spectrum of minimal blocking sets in Galois planes of non‐prime order is also presented. The most attractive case is when q is a square, where we show that there is a minimal blocking set for any size from the interval $[4q,{\rm log}, q, q\sqrt q-q+2\sqrt q]$. © 2004 Wiley Periodicals, Inc. J Combin Designs 13: 25–41, 2005.

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