Hilbert Bases for Orthogonal Arrays

Abstract

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 theoretically solved by means of Hilbert bases which form a finite generating set for all the elements in in the infinite set OA$(n,m)$. We discuss some examples which are explicitly solved with a software performing Hilbert bases computation.