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.
Classification of some large sets and designs
β Scribed by Ziba Eslami; Gholamreza B. Khosrovshahi
- Book ID
- 105124706
- Publisher
- Springer
- Year
- 2000
- Tongue
- English
- Weight
- 257 KB
- Volume
- 67
- Category
- Article
- ISSN
- 0047-2468
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## 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.