Triple arrays and related designs

We consider a problem posed by Donald Preece more than 30 years ago. Let S be a set of 35 distinct elements. Construct a 7×15 rectangular array A, each of whose entries is a member of S, with no symbol repeated in any row or column, with the following properties: (P1)each symbol occurs precisely thr...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2014-01, Vol.163, p.220-236
Main Author: Wallis, W.D.
Format: Article
Language:English
Subjects:
Array
Arrays
Block design
Construction
Mathematical analysis
Symbols
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Summary:We consider a problem posed by Donald Preece more than 30 years ago. Let S be a set of 35 distinct elements. Construct a 7×15 rectangular array A, each of whose entries is a member of S, with no symbol repeated in any row or column, with the following properties: (P1)each symbol occurs precisely three times in the array;(P2)any two distinct rows contain precisely five common symbols;(P3)any two distinct columns contain precisely one common symbol;(P4)any row and any column contain precisely three common symbols. We shall present a solution, survey related work, and look toward further problems.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2013.04.010