A note on construction of nearly uniform designs with large number of runs

Uniform designs have been used in computer experiments (Fang et al., Technometrics 42 (2000) 237). A uniform design seeks its design points to be uniformly scattered on the experimental domain. When the number of runs is large, to search a related uniform design is a NP hard problem. Therefore, the number of runs of most existing uniform designs is small ([less-than-or-equals, slant]50). In this article, we propose a way to construct nearly uniform designs with large number of runs by collapsing two uniform designs in the sense of low-discrepancy. The number of runs of the novel design is the product of the two numbers of runs of both original designs. Two measures of uniformity, the centered L2-discrepancy (CD) and wrap-around L2-discrepancy (WD) are employed. Analytic formulas of CD- and WD-values between the novel design and both original designs are obtained.