Nested nearly orthogonal Latin hypercube designs for many design columns

Nested Latin hypercube designs are widely employed for conducting multiple computer experiments with varying levels of fidelity. In the context of polynomial function models, achieving orthogonality is particularly important, as it enables uncorrelated estimation of linear effects under a first-order model. Therefore, maintaining low inter-factor correlation is a highly desirable property in design construction. In this paper, we propose a novel method for constructing nested nearly orthogonal Latin hypercube designs with flexible design columns and low inter-factor correlations. Comparative studies with existing nested Latin hypercube designs demonstrate that the proposed designs achieve lower inter-factor correlations and require fewer runs, making them more efficient and cost-effective for practical applications.