A S(3, {4, 6}, 18) with a subdesign S(3, 4, 8) does not exist

✍ Scribed by Vaclav Linek

• Book ID: 102308942
• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 72 KB
• Volume: 17
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20176

✦ Synopsis

Abstract

For $K \subset {1,2,3,\ldots}$, a S(t,K,v) design is a pair, $(V,{\cal B})$, with |V| = v and ${\cal B}$ a set of subsets of V such that each t‐subset of V is contained in a unique $\alpha \in {\cal B}$ and $\vert \alpha \vert \in K$ for all $\alpha \in {\cal B}$. If $U \subseteq V$, $\vert U\vert=u$, ${\cal A}={\alpha\in{\cal B} : \alpha\subseteq U}$, and $(U,{\cal A})$ is a S(t,K,u) design, then we say $(V,{\cal B})$ has a subdesign on U. We show that a S(3,{4,6},18) design with a subdesign S(3,4,8) does not exist. © 2007 Wiley Periodicals, Inc. J Combin Designs 17: 36–38, 2009