Abstract: Intended for computer experiments with both qualitative and quantitative factors, marginally coupled designs were introduced by Deng, Hung and Lin (2015) as a more economical strategy than the original, sliced space-filling designs. Among the designs constructed in Deng, Hung and Lin (2015), the corresponding designs for quantitative factors possess only the one-dimensional space-filling property with respect to each level of any factor in designs for qualitative factors. In addition, their designs for quantitative factors have clustered points. To avoid clustered points and enhance two- and higher-dimensional space-filling property in designs for quantitative factors, we propose three approaches to construct marginally coupled designs. Theoretical results of marginally coupled designs are also derived.

Key words and phrases: Cascading Latin hypercube, completely resolvable, Latin hypercube, orthogonal array, projection, Rao-Hamming construction, space-filling.