Construction of maximum projection Latin hypercube designs using number-theoretic methods

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 (Formula presented.) -distance, and the uniform projection criterion.