Lower bounds on the size of t-fold blocking sets with respect to hyperplanes or t-intersection sets in AG(n, q) are obtained, some of which are sharp.
On Nuclei and Blocking Sets in Desarguesian Spaces
✍ Scribed by Simeon Ball
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 89 KB
- Volume
- 85
- Category
- Article
- ISSN
- 0097-3165
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✦ Synopsis
A generalisation is given to recent results concerning the possible number of nuclei to a set of points in PG(n, q). As an application of this we obtain new lower bounds on the size of a t-fold blocking set of AG(n, q) in the case (t, q)>1.
📜 SIMILAR VOLUMES
In this paper we show that blocking sets of cardinality less than 3(q ϩ 1)/2 (q ϭ p n ) in Desarguesian projective planes intersect every line in 1 modulo p points. It is also shown that the cardinality of a blocking set must lie in a few relatively short intervals. This is similar to previous resul
The characterisation by Blokhuis, Ball, Brouwer, Storme, and Szönyi of certain kinds of blocking sets of Rédei type is extended to specify the type of polynomial which defines the blocking set. A graphic characterisation called the profile of the set is also given, and the correspondence between the
## Abstract Let __S__ be a blocking set in an inversive plane of order __q__. It was shown by Bruen and Rothschild 1 that |__S__| ≥ 2__q__ for __q__ ≥ 9. We prove that if __q__ is sufficiently large, __C__ is a fixed natural number and |__S__ = 2__q__ + __C__, then roughly 2/3 of the circles of the
## Abstract In this paper, we show that there are at least __cq__ disjoint blocking sets in PG(2,__q__), where __c__ ≈ 1/3. The result also extends to some non‐Desarguesian planes of order __q__. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 149–158, 2006
## 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‐p