Algorithmic construction of nearly column-orthogonal designs

Computer models can describe complicated phenomena encountered in science and engineering fields. To use these models for scientific investigation, however, their generally long running time and mostly deterministic nature require a specially designed experiment. The column-orthogonal design (COD) is a popular choice for computer experiments. Because of the restriction on the orthogonality, however, only little CODs can be constructed. In this article, we propose two algorithms for constructing nearly CODs by rotating orthogonal arrays under two different criteria. Further, some obtained nearly CODs are nearly Latin hypercube designs. Some examples are provided to show the advantages of our algorithms. Some rotation matrices obtained via the algorithms are listed.