We show that binary designs for cross-over models obtained from orthogonal arrays are universally optimal under correlated errors. Some key words: Carry-over effect; Change-over design; Cross-over design; Dependent observations; Generalized least-squares; Optimal design; Orthogonal arrays; Repeated measurements design.

There is a famous construction of orthogonal arrays by R.C. Bose (1947). The construction uses linear transformations over a finite field. We generalize this to use non-linear transformation instead of linear and a subset of vector space as their domains. We show here constructions of orthogonal and balanced arrays which are generated by a set of quadratic function.

In this paper, we provide a generalization of the classical Rao bound for orthogonal arrays, which can be applied to ordered orthogonal arrays and (t; m; s)-nets. Application of our new bound leads to improvements in many parameter situations to the strongest bounds (i.e., necessary conditions) for existence of these objects.

The generalized word length pattern of an orthogonal array allows a ranking of orthogonal arrays in terms of the generalized minimum aberration criterion (Xu and Wu [Ann. Statist. 29 (2001) 1066–1077]). We provide a statistical interpretation for the number of shortest words of an orthogonal array in terms of sums of R2 values (based on orthogonal coding) or sums of squared canonical correlatio...

A simple orthogonal array OA(q2n−1, q2n−2, q, 2) is constructed by using the action of a large subgroup of PGL(n + 1, q2) on a set of non degenerate Hermitian varieties in PG(n, q2).

In this paper, we relate the problem of generating all 2-level orthogonal arrays of given dimension and force, i.e. elements in OA(n, m), where n is the number of factors and m the force, to the solution of an Integer Programming problem involving rational convex cones. We do not restrict the number of points in the array, i.e. we admit any number of replications. This problem can be theoretica...