Proper S(t, K,v)'s for t ≥ 3,v ≤ 16, |K| > 1 and Their Extensions

✍ Scribed by E. S. Kramer; Rudolf Mathon

• Publisher: John Wiley and Sons
• Year: 1995
• Tongue: English
• Weight: 872 KB
• Volume: 3
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.3180030606

✦ Synopsis

We characterize the proper t-wise balanced designs t-(v,K.l) for t 2 3, A = 1 and v 5 16 with at least two block sizes. While we do not examine extensions of S(3,4,16)'s, we do determine all other possible extensions of S ( 3 , x , v ) ' s for v 5 16. One very interesting extension is an 5(4,{5,6}, 17) design. 0 1995 John Wiley & Sons, Inc.

1. Introduction

A t-wise balanced design (tBD) of type t -( v , x , A ) is a pair ( X , B ) where X is a v-element set of points and 2 3 is a collection of subsets of X called blocks with the property that the size of every block is in K and every t-element subset of X is contained in exactly A blocks. If x is a set of positive integers strictly between t and v then we say the tBD is proper. A t-(v, K , A) design is also denoted by Sn(t, K , v). If ) K ) = 1, then the tBD is called a t-(v, k , A) design, where K = {k}. If A = 1, then we often use the notation S ( t , X , v ) .