Recent researches on designs for computer experiments with both qualitative and quantitative factors have advocated the use of marginally coupled designs. This paper proposes a general method of constructing such designs for which the designs for qualitative factors are multi-level orthogonal arrays and the designs for quantitative factors are Latin hypercubes with desirable space-filling properties. Two cases are introduced for which we can obtain the guaranteed low-dimensional space-filling property for quantitative factors. Theoretical results on the proposed constructions are derived. For practical use, some constructed designs for three-level qualitative factors are tabulated.
"Construction of marginally coupled designs by subspace theory." Bernoulli 25 (3) 2163 - 2182, August 2019. https://doi.org/10.3150/18-BEJ1049