We develop a new method for constructing "good" designs for computerexperiments. The method derives its power from its basic structure that buildslarge designs using small designs. We specialize the method for theconstruction of orthogonal Latin hypercubes and obtain many results along theway. In terms of run sizes, the existence problem of orthogonal Latinhypercubes is completely solved. We also present an explicit result showing howlarge orthogonal Latin hypercubes can be constructed using small orthogonalLatin hypercubes. Another appealing feature of our method is that it can easilybe adapted to construct other designs; we examine how to make use of the methodto construct nearly orthogonal and cascading Latin hypercubes.
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