U-type and column-orthogonal designs for computer experiments

U-type designs and orthogonal Latin hypercube designs (OLHDs) have been used extensively for performing computer experiments. Both have good spaced filling properties in one-dimension. U-type designs may not have low correlations among the main effects, quadratic effects and two-factor interactions. On the other hand, OLHDs are hard to be found due to their large number of levels for each factor. Recently, alternative classes of U-type designs with zero or low correlations among the effects of interest appear in the literature. In this paper, we present new classes of U-type or quantitative 3-orthogonal designs for computer experiments. The proposed designs are constructed by combining known combinatorial structures and they have their main effects pairwise orthogonal, orthogonal to the mean effect, and orthogonal to both quadratic effects and two-factor interactions