On the maximin distance properties of orthogonal designs via the rotation

Space-filling designs are widely used in computer experiments. They are frequently evaluated by the orthogonality and distance-related criteria. Rotating orthogonal arrays is an appealing approach to constructing orthogonal space-filling designs. An important issue that has been rarely addressed in the literature is the design selection for the initial orthogonal arrays. This paper studies the maximin L₂-distance properties of orthogonal designs generated by rotating two-level orthogonal arrays under three criteria. We provide theoretical justifications for the rotation method from a maximin distance perspective and further propose to select initial orthogonal arrays by the minimum G₂-aberration criterion. New infinite families of orthogonal or 3-orthogonal U-type designs, which also perform well under the maximin distance criterion, are obtained and tabulated. Examples are presented to show the effectiveness of the constructed designs for building statistical surrogate models.