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