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