Optimal design of experiments with quantitative-sequence factors

A new type of experiment with joint considerations of quantitative and sequence factors is recently drawing much attention in medical science, bio-engineering, and many other disciplines. The input spaces of such experiments are semi-discrete and often very large. Thus, efficient and economical experimental designs are required. Based on the transformations and aggregations of good lattice point sets, we construct a new class of optimal quantitative-sequence (QS) designs that are marginally coupled, pair-balanced, space-filling, and asymptotically orthogonal. The proposed QS designs have a certain flexibility in run and factor sizes and are especially appealing for high-dimensional cases.