A New Approach to Construction of Nearly Uniform Designs

The uniform design is one of space filling designs and has been widely used in computer and industrial experiments. Many methods for construction of uniform designs or nearly uniform designs, such as the glp method, optimization method etc. have been proposed. A nearly uniform design is a design with low-discrepancy, where the discrepancy is a measure of uniformity. Various discrepancies have been suggested. To find a uniform design for n runs and s factors under a given discrepancy is a NP hard problem in the sense of computation complexity when n → ∞ and s > 1. In this paper we propose a new method, called the cutting method, for construction of nearly uniform designs. It shows that the computation load of the new method is light and designs obtained by the new approach have better uniformity.