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

Abstract

AbstractThe size of large minimal blocking sets is bounded by the Bruen–Thas upper bound. The bound is sharp whenqis a square. Here the bound is improved ifqis 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, ifqis a cube, then our construction gives minimal blocking sets of sizeq4/3 + 1 orq4/3 + 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 whenqis 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.