Contents

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Double Youden rectangles of sizes p×(2p+1) and (p+1)×(2p+1)

D.A. Preece1, B.J. Vowden1, N.C.K. Phillips2
1Institute of Mathematics and Statistics University of Kent at Canterbury Canterbury, Kent CT2 7NF, UK
2 Department of Computer Science Southern Illinois University Carbondale, Illinois USA 62901

Abstract

A k×v double Youden rectangle (DYR) is a type of balanced Graeco-Latin design where each Roman letter occurs exactly once in each of the k rows, where each Greek letter occurs exactly once in each of the v columns, and where each Roman letter is paired exactly once with each Greek letter. The other properties of a DYR are of balance, and indeed the structure of a DYR incorporates that of a symmetric balanced incomplete block design (SBIBD). Few general methods of construction of DYRs are known, and these cover only some of the sizes k×v with k=p (odd) or p+1, and v=2p+1. Computer searches have however produced DYRs for those such sizes, p11, for which the existence of a DYR was previously in doubt. The new DYRs have cyclic structures. A consolidated table of DYRs of sizes p×(2p+1) and (p+1)×(2p+1) is provided for p11; for each of several of the sizes, DYRs are given for different inherent SBIBDs.