Blocking Sets of Size qt+qt−1+1

✍ Scribed by G. Lunardon; O. Polverino

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 125 KB
• Volume: 90
• Category: Article
• ISSN: 0097-3165
• DOI: 10.1006/jcta.1999.3022

✦ Synopsis

We prove that in the desarguesian plane PG(2, q t ) (t>4) there are at least three inequivalent blocking sets of size q t +q t&1 +1. The first one has q+1 Re dei lines, the second one has exactly one Re dei line, and the third one is not of Re dei type. For GF(q) the largest subfield of GF(q t ), our results disprove a conjecture quoted by A. Blokhuis (1998, in ``Galois Geometry and Generalized Polygons,'' Gent).

2000 Academic Press are called small. They intersect every line in a number of points congruent to 1 modulo p (see [12]).

It has been proved by Bruen in [3] that a blocking set B has size |B| q+-q+1, and equality holds if and only if B is a Baer subplane. Therefore, in a desarguesian plane of square order, all the blocking sets of minimum size are equivalent.