Abstract: Latin hypercube designs (LHDs) have found wide applications in computer experiments. Some methods have been proposed to construct orthogonal (or nearly orthogonal) LHDs. This paper proposes methods for expanding a fold-over orthogonal (or nearly orthogonal) LHD to a nearly orthogonal LHD which is able to accommodate many factors. The number of factors is flexible and can be almost as twice large as the number of factors of the original LHD, while the run size remains unchanged. It is shown that the upper bound of the maximum correlation between any two distinct columns of the resulting design is very small (smaller than 0.10 for most cases). The proposed methods can be applied to any fold-over LHDs.

Key words and phrases: Computer experiment, correlation, Latin hypercube design, orthogonality.