Marginally coupled designs for two-level qualitative factors

Computer experiments with qualitative and quantitative factors occur frequently in various applications in science, engineering and business. For choosing input settings of such computer experiments, marginally coupled designs have been proposed in Deng, Hung and Lin (2015) for economic reasons. Although the concept of marginally coupled designs is well understood, the results on design construction are scarce. In addition, the constructed designs may have clustered points for the quantitative factors or cannot accommodate many quantitative factors, especially for two-level qualitative factors. To address this issue, this paper focuses on constructing marginally coupled designs when all qualitative factors have two levels. The proposed construction uses subspace theory in algebra, and the resulting designs can accommodate more quantitative factors while maintaining attractive design properties than the existing approaches.