Pairwise Orthogonal F-Rectangle Designs

摘要

The concept of pairwise orthogonal Latin square designs 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 simultaneous 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 treatments (symbols), whereas no pair of orthogonal Latin square designs of orders two and six exists, and 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 designs. 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 sub n columns, (v sub n - 1)/(v - 1) rows, v symbols, and of strength two. (Author)