Starting out from the 15 pairs of opposite edges and the 20 faces of a coloured icosahedron , a simple new construction is given of a 'double-five' of planes in PG (5 , 2) . This last is a recently discovered configuration consisting of a set of (15 ฯฉ 20 ฯญ )35 points in PG (5 , 2) which admits five
Intersection-sets in PG(n,2)
โ Scribed by Aiden Bruen; Lucien Haddad; David Wehlau
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 450 KB
- Volume
- 62
- Category
- Article
- ISSN
- 0378-3758
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
## Abstract Bruen and Thas proved that the size of a large minimal blocking set is bounded by $q \cdot {\sqrt{q}} + 1$. Hence, if __q__โ=โ8, then the maximal possible size is 23. Since 8 is not a square, it was conjectured that a minimal blocking 23โset does not exist in PG(2,8). We show that this
## Abstract The size of large minimal blocking sets is bounded by the BruenโThas upper bound. The bound is sharp when __q__ is a square. Here the bound is improved if __q__ is a nonโsquare. On the other hand, we present some constructions of reasonably large minimal blocking sets in planes of nonโp
## Abstract A tangency set of PG __(d,q)__ is a set __Q__ of points with the property that every point __P__ of __Q__ lies on a hyperplane that meets __Q__ only in __P__. It is known that a tangency set of PG __(3,q)__ has at most $q^2+1$ points with equality only if it is an ovoid. We show that a