Lower bound of average centered L2-discrepancy for U-type designs

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.

KEYWORDS:

• Average centered L₂-discrepancy
• Generalized minimum aberration
• Level permutation
• Uniform designs
• U-type designs.

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 62K15
• Secondary: 62K20

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).

Additional information

Funding

China Postdoctoral Science Foundation (2017M611147) National Natural Science Foundation of China 11471239,11501405,11601366,11601367