Construction of Orthogonal Nearly Latin Hypercubes

Orthogonal Latin hypercubes (OLHs) are available for only a limited collection of run sizes. This paper presents a simple algorithm for constructing orthogonal designs that are nearly Latin hypercubes. The algorithm is based on the approach developed by Steinberg and Lin for OLH designs and can generate designs for all run sizes for which a Plackett-Burman design exists. The designs have good univariate projections, although they are not perfectly uniform. They also provide good spatial coverage in higher dimensions. The great gain in sample size flexibility requires just a small sacrifice in the univariate spread of points.