Strong orthogonal Latin hypercubes for computer experiments

Orthogonal Latin hypercubes are widely used for computer experiments. They achieve both orthogonality and the maximum one-dimensional stratification property. When two-factor (and higher-order) interactions are active, two- and three-dimensional stratifications are also important. Unfortunately, little is known about orthogonal Latin hypercubes with good two (and higher)–dimensional stratification properties. A method is proposed for constructing a new class of orthogonal Latin hypercubes whose columns can be partitioned into groups, such that the columns from different groups maintain two- and three-dimensional stratification properties. The proposed designs perform well under almost all popular criteria (e.g., the orthogonality, stratification, and maximin distance criterion). They are the most ideal designs for computer experiments. The construction method can be straightforward to implement, and the relevant theoretical supports are well established. The proposed strong orthogonal Latin hypercubes are tabulated for practical needs.