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Some existence theorems for t-designs

✍ Scribed by Tran van Trung

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
640 KB
Volume
128
Category
Article
ISSN
0012-365X

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✦ Synopsis

We generalize some existence theorems for t- (u,k,l) designs. In fact, we prove that if certain inequality holds involving parameters of some simple r-designs, then new simple t-designs can be constructed.

Using these results we discover first examples of infinite families of 5-designs in which blocks always intersect in less than (k -1) points.

πŸ“œ SIMILAR VOLUMES

An existence theorem for some simple t-d
An existence theorem for some simple t-designs
✍ Michel Dehon πŸ“‚ Article πŸ“… 1991 πŸ› Elsevier Science 🌐 English βš– 314 KB

Dehon, M., An existence theorem for some simple t-designs, Discrete Mathematics 90 (1991) 137-142. ## Let S' be a simple S;(t, k, [) containing b' blocks and let S be a, not necessarily simple, $(t, 1. u); we prove that if b"(A -1) < (:), then there exists a simple &,(t, k, v). We apply this resu

Some results on the existence of large s
Some results on the existence of large sets of t-designs
✍ 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