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A few more large sets of t-designs

✍ 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.

✦ 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.


πŸ“œ SIMILAR VOLUMES


New large sets of t-designs
✍ Reinhard Laue; Spyros S. Magliveras; Alfred Wassermann πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 170 KB
Some Infinite Families of Large Sets of
✍ B. Tayfeh-Rezaie πŸ“‚ Article πŸ“… 1999 πŸ› Elsevier Science 🌐 English βš– 98 KB

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.

Some results on the existence of large s
✍ G. B. Khosrovshahi; R. Tayfeh-Rezaie πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 96 KB πŸ‘ 1 views

## Abstract A set of trivial necessary conditions for the existence of a large set of __t__‐designs, __LS__[N](__t,k,__Ξ½), is $N\big | {{\nu \hskip -3.1 \nu}-i \choose k-i}$ for __i__ = 0,…,__t__. There are two conjectures due to Hartman and Khosrovshahi which state that the trivial necessary condi

New large sets of t-designs with prescri
✍ R. Laue; G. R. Omidi; B. Tayfeh-Rezaie; A. Wassermann πŸ“‚ Article πŸ“… 2007 πŸ› John Wiley and Sons 🌐 English βš– 128 KB πŸ‘ 1 views

## Abstract In this article, we investigate the existence of large sets of 3‐designs 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

Large sets of disjoint group-divisible d
✍ H. Cao; J. Lei; L. Zhu πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 141 KB πŸ‘ 1 views

## Abstract Large sets of disjoint group‐divisible 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

Existence of large sets of disjoint grou
✍ L. Ji πŸ“‚ Article πŸ“… 2005 πŸ› John Wiley and Sons 🌐 English βš– 142 KB πŸ‘ 2 views

## Abstract Large sets of disjoint group‐divisible designs with block size three and type 2^__n__^4^1^ (denoted by __LS__ (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