On the existence and constructions of orthogonal designs

This paper presents some new results on orthogonal designs, which are a useful class of designs for computer experiments. We first establish a non-existence result on orthogonal designs, generalising an earlier known result on orthogonal Latin hypercubes, and then present some construction results. By computer search, we obtain a collection of orthogonal designs with small run sizes. Using these results and existing methods in the literature, we compile a comprehensive catalogue of orthogonal designs for up to 100 runs.