Abstract: Marginally coupled designs (MCDs) are well-suited for computer experiments with both qualitative and quantitative factors. In this paper, we construct a new class of MCDs via the Rao-Hamming construction. Moreover, we show that the designs for quantitative factors in such MCDs are not only column-orthogonal, but also strong orthogonal arrays of strength 2*. Building on these results, we further obtain a series of MCDs with more flexible run sizes.