Pairwise orthogonal F-rectangle designs (Q801069)

This paper applies the concept of orthogonal Latin squares to F-rectangle designs. Several results are obtained, among others: (i) A pair of orthogonal F-rectangle designs exists for any set of v treatments; (ii) Complete sets of orthogonal F-rectangle designs exist for all v for which v is a prime power; (iii) t orthogonal F-rectangle designs exist if t orthogonal Latin squares exist; (iv) Complete sets of orthogonal F- rectangle designs are constructed for \(v=2\) in 2 rows and 4k columns if a Hadamard matrix of order 4k exists. Some applications are presented to codes and orthogonal arrays.