Abstract
Uniform designs are widely used in various applications. However, it is computationally intractable to construct uniform designs, even for moderate number of runs, factors and levels. We establish a linear relationship between average squared centered L2-discrepancy and generalized wordlength pattern, and then based on it, we propose a general method for constructing uniform designs with arbitrary number of levels. The main idea is to choose a generalized minimum aberration design and then permute its levels. We propose a novel stochastic algorithm and obtain many new uniform designs that have smaller centered L2-discrepancies than the existing ones.
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