Mirror-Symmetric Orthogonal Latin Hypercubes with Attractive Space-Filling Properties

Computer experiments have been widely used to build high-quality surrogate models for complex emulation systems.Orthogonal Latin hypercubes are efficient designs for computer experiments as they enjoy both orthogonality and one-dimensional maximum stratification.Mirror symmetric designs have also been advocated for computer experiments.The mirror-symmetry structure can yield higher-order orthogonality and significantly benefit the identification of the main and interaction effects.The construction of mirror-symmetric orthogonal Latin hypercubes is limited and challenging.This paper proposes a construction method for mirror-symmetric orthogonal Latin hypercubes using orthogonal arrays from Reed-Solomon codes.Theoretical results guarantee that the resulting designs enjoy attractive orthogonality and low-dimensional space-filling properties.Moreover, some of the resulting designs are optimal under the maximin distance criterion.Simulation comparisons are also provided to demonstrate the superiority of the proposed designs over existing designs.