An effective construction method for multi-level uniform designs

• Average squared centered L2-discrepancy is a linear combination of generalized wordlength pattern.
• A general method is proposed for constructing uniform designs.
• A novel stochastic algorithm is proposed.
• New uniform designs with low centered L2-discrepancies are obtained.

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.