Construction of Uniform Projection Designs

In computer experiments, space-filling designs with favourable low-dimensional projection properties are crucial for the efficient exploration of the design space, especially when many factors are involved but only a few are active. Among existing space-filling designs, uniform projection designs stand out for their guaranteed uniformity across all two-dimensional projections. This paper presents a series of novel and efficient algebraic constructions for uniform projection designs. By using orthogonal arrays, permuted good lattice point designs and -equidistant designs, we generate a rich class of uniform projection designs with flexible sizes. Additionally, we construct column-orthogonal designs that are also nearly optimal under the uniform projection criterion. Numerical comparisons demonstrate the superiority of our proposed constructions compared to existing methods.