Pairwise orthogonal F-rectangle designs

• Published in: Journal of statistical planning and inference 1984-01, Vol.10 (3), p.365-374
• Main Authors: Federer, W.T., Hedayat, A.S., Mandeli, J.P.
• Format: Article
• Language: English
• Subjects: Codes; Complete sets; Orthogonal arrays; Pairwise orthogonal Latin squares; Simultaneous and/or sequential experiments
• ISSN: 0378-3758; 1873-1171
• DOI: 10.1016/0378-3758(84)90060-0

The concept of pairwise orthogonal Latin square design is applied to r row by c column experiment designs which are called pairwise orthogonal F-rectangle designs. These designs are useful in designing successive and/or simulataneous experiments on the same set of rc experimental units, in constructing codes, and in constructing orthogonal arrays. A pair of orthogonal F-rectangle designs exists for any set of v treatment (symbols), whereas no pair of orthogonal Latin square designs of order two and six exists; one of the two construction methods presented does not rely on any previous knowledge about the existence of a pair of orthogonal Latin square designs, whereas the second one does. It is shown how to extend the methods to r= pv row by c= qv column designs and how to obtain t pairwise orthogonal F-rectangle design. When the maximum possible number of pairwise orthogonal F-rectangle designs is attained the set is said to be complete. Complete sets are obtained for all v for which v is a prime power. The construction method makes use of the existence of a complete set of pairwise orthogonal Latin square designs and of an orthogonal array with v n columns, ( v n −1)/( v−1) rows, v symbols, and of strength two.