A few more large sets of t-designs
β Scribed by Yeow Meng Chee; Spyros S. Magliveras
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 176 KB
- Volume
- 6
- Category
- Article
- ISSN
- 1063-8539
No coin nor oath required. For personal study only.
β¦ Synopsis
We construct several new large sets of t-designs that are invariant under Frobenius groups, and discuss their consequences. These large sets give rise to further new large sets by means of known recursive constructions including an infinite family of large sets of 3 -(v, 4, Ξ») designs.
π SIMILAR VOLUMES
A set of necessary conditions for the existence of a large set of t-designs, LS[N] (t, k, v), is N |( v&i k&i ) for i=0, 1, ..., t. We show that these conditions are sufficient for N=3, t=2, 3, or 4, and k 8.
## Abstract A set of trivial necessary conditions for the existence of a large set of __t__βdesigns, __LS__[N](__t,k,__Ξ½), is $N\big | {{\nu \hskip -3.1 \nu}-i \choose k-i}$ for __i__β=β0,β¦,__t__. There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary condi
## Abstract In this article, we investigate the existence of large sets of 3βdesigns of prime sizes with prescribed groups of automorphisms PSL(2,__q__) and PGL(2,__q__) for __q__ < 60. We also construct some new interesting large sets by the use of the computer program DISCRETA. The results obtain
## Abstract Large sets of disjoint groupβdivisible designs with block size three and type 2^__n__^4^1^ have been studied by Schellenberg, Chen, Lindner and Stinson. These large sets have applications in cryptography in the construction of perfect threshold schemes. It is known that such large sets
## Abstract Large sets of disjoint groupβdivisible designs with block size three and type 2^__n__^4^1^ (denoted by __LS__β(2^__n__^4^1^)) were first studied by Schellenberg and Stinson and motivated by their connection with perfect threshold schemes. It is known that such large sets can exist only