On the Size of a Double Blocking Set inPG(2,q)
β Scribed by Simeon Ball; Aart Blokhuis
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 212 KB
- Volume
- 2
- Category
- Article
- ISSN
- 1071-5797
No coin nor oath required. For personal study only.
β¦ Synopsis
We obtain lower bounds for the size of a double blocking set in the Desarguesian projective plane PG(2, q). These bounds are best possible for q Ο½ 11 and in the case q is a square. With the same technique we also exclude certain values for the size of an ordinary minimal blocking set.
π SIMILAR VOLUMES
We prove that the number of directions determined by a set of p points in AG(2, p), p prime, cannot be between ( p+3)Γ2 and ( p&1)Γ2+ 1 3 -p. This is equivalent to saying that besides the projective triangle, every blocking set of Re dei type in PG(2, p) has size at least 3( p&1)Γ2+ 1 3 -p.
## Abstract In a previous paper 1, all point sets of minimum size in __PG__(2,__q__), blocking all external lines to a given irreducible conic ${\cal C}$, have been determined for every odd __q__. Here we obtain a similar classification for those point sets of minimum size, which meet every externa
Let v, k be positive integers and k β₯ 3, then K k = {v : v β₯ k} is a 3-BD closed set. Two finite generating sets of 3-BD closed sets K 4 and K 5 are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v β₯ 6, then v β B 3 (K, 1), where K = {6, 7, . . . , 41, 45
An infinite family of minimal blocking sets of H(3,q 2 ) is constructed for even q, with links to Ceva configurations.
Let be a finite subset of the Cartesian product W 1 Γ β’ β’ β’ Γ W n of n sets. For A β {1, 2, . . . , n}, denote by A the projection of onto the Cartesian product of W i , i β A. Generalizing an inequality given in an article by Shen, we prove that , 2, . . . , n}. This inequality is applied to give s