Sequential Latin hypercube designs have recently received great attention for computer experiments. Much of the work has been restricted to invariant spaces. The related systematic construction methods are inflexible while algorithmic methods are ineffective for large designs. For such designs in space contraction, systematic construction methods have not been investigated yet. This paper proposes a new method for constructing sequential Latin hypercube designs via good lattice point sets in a variety of experimental spaces. These designs are called sequential good lattice point sets. Moreover, we provide fast and efficient approaches for identifying the (nearly) optimal sequential good lattice point sets under a given criterion. Combining with the linear level permutation technique, we obtain a class of asymptotically optimal sequential Latin hypercube designs in invariant spaces where the $L_1$-distance in each stage is either optimal or asymptotically optimal. Numerical results demonstrate that the sequential good lattice point set has a better space-filling property than the existing sequential Latin hypercube designs in the invariant space. It is also shown that the sequential good lattice point sets have less computational complexity and more adaptability.

翻译：序贯拉丁超立方设计近年来在计算机试验中备受关注。但现有工作大多局限于不变空间，其系统构建方法缺乏灵活性，而算法方法在处理大规模设计时效率低下。针对空间收缩中的此类设计，目前尚未开展系统构建方法的研究。本文提出一种新方法，通过在不同试验空间中使用好格子点集来构建序贯拉丁超立方设计，称为序贯好格子点集。此外，我们提供了快速高效的策略，用于在给定准则下识别（近）最优序贯好格子点集。结合线性水平置换技术，我们得到一类在不变空间中具有渐近最优性的序贯拉丁超立方设计，其中各阶段的$L_1$距离达到最优或渐近最优。数值结果表明，在不变空间中，序贯好格子点集比现有序贯拉丁超立方设计具有更好的空间填充性质，且计算复杂度更低、适应性更强。