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.

翻译：近年来，一种同时考虑定量因子与序列因子的新型实验在医学、生物工程及诸多其他学科领域受到广泛关注。此类实验的输入空间具有半离散特性且通常规模极大，因此需要高效且经济的实验设计方案。基于良好格点集的变换与聚合，我们构建了一类新的最优定量-序列（QS）设计，该类设计具有边际耦合性、配对平衡性、空间填充性及渐近正交性。所提出的QS设计在实验次数与因子数量方面具备一定的灵活性，尤其适用于高维情形。