## Abstract A __large set__ of Kirkman triple systems of order __v__, denoted by __LKTS__(__v__), is a collection {(__X__, __B~i~__) : 1ββ€β__i__ββ€β__v__βββ2}, where every (__X__,__B~i~__) is a __KTS__(__v__) and all __B~i~__ form a partition of all triples on __X__. Many researchers have studied th
Some Infinite Families of Large Sets of t-Designs
β Scribed by B. Tayfeh-Rezaie
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 98 KB
- Volume
- 87
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
β¦ Synopsis
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.
π SIMILAR VOLUMES
## 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
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.
## 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 A Menon design of order __h__^2^ is a symmetric (4__h__^2^,2__h__^2^β__h__,__h__^2^β__h__)βdesign. Quasiβresidual and quasiβderived designs of a Menon design have parameters 2β(2__h__^2^β+β__h__,__h__^2^,__h__^2^β__h__) and 2β(2__h__^2^β__h__,__h__^2^β__h__,__h__^2^β__h__β1), respective