Construction of maximum projection Latin hypercube designs using number‐theoretic methods
提出两种基于数论和好格子点设计的代数构造方法，生成最大投影拉丁超立方设计，在投影性质上渐近最优且接近下界，同时具备优良的正交性和均匀性，适用于只有部分因子活跃的计算机实验。
Abstract Maximum projection (MaxPro) Latin hypercube designs (LHDs) are appealing for computer experiments where only a subset of the design factors are active. These designs are distinguished by their ability to optimize projection properties across all possible subsets of factors. However, the construction of MaxPro LHDs remains a challenging problem, and existing literature on the subject is limited. This paper presents two algebraic construction methods for MaxPro LHDs, based on good lattice point designs and number theory. The resulting designs are asymptotically optimal in terms of log‐distance and nearly optimal in achieving the MaxPro lower bounds. Furthermore, they demonstrate excellent multi‐criteria performance in terms of column orthogonality, maximin ‐distance, and the uniform projection criterion.