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来在计算机实验中备受关注，但相关研究多局限于不变空间。现有系统构造方法缺乏灵活性，而算法方法对于大规模设计效果不佳。针对空间收缩中的此类设计，目前尚未有系统构造方法的研究。本文提出一种通过优格点集在不同实验空间中构造序贯拉丁超立方设计的新方法，这类设计被称为序贯优格点集。此外，我们提供了在给定准则下快速高效识别（近）最优序贯优格点集的方法。结合水平线性置换技术，我们在不变空间中获得了一类渐近最优的序贯拉丁超立方设计，其中每个阶段的 $L_1$ 距离达到最优或渐近最优。数值结果表明，与现有不变空间中的序贯拉丁超立方设计相比，序贯优格点集具有更优的空间填充性质，并展现出更低的计算复杂度和更强的适应性。