ABSTRACT
Uniform designs are widely used in various scientific investigations and industrial applications. By considering all possible level permutation of the factors, a connection between average centered L2-discrepancy and generalized wordlength pattern for asymmetrical fractional factorial designs is derived. Moreover, we present new lower bounds to the average centered L2-discrepancy for symmetrical and asymmetrical U-type designs. For illustration of the theoretical results, the lower bounds for symmetrical and asymmetrical U-type designs are tabulated, and numerical results indicate that our lower bounds behave well and can be recommended for use in practice.
MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
This work was supported by the National Natural Science Foundation of China (Grant No. 11601366, 11471239, 11501405, 11601367), the Postdoctoral Science Foundation funded project of China (Grant No. 2017M611147).