Minimum aberration 4¹2ⁿ designs via secondary complementary sets

Abstract

Mixed-level designs are widely used in various experiments. This paper considers how to construct minimum aberration $4^1{2}^n$ mixed-level designs. Based on finite projective geometry, secondary complementary set is defined as part of the design which plays a crucial role in constructing the optimal designs. Then, algebraic connection between the wordlength pattern of a $4^1{2}^n$ design and that of its secondary complementary set is established. According to the connection, some general rules for identifying type 0 minimum aberration $4^1{2}^n$ mixed-level designs are proposed via their secondary complementary sets. Those rules can help construct minimum aberration $4^1{2}^n$ designs conveniently when the secondary complementary set contains fewer elements than the complementary set. The type 0 minimum aberration $4^1{2}^n$ designs with large n are tabulated via secondary complementary sets.

KEYWORDS:

• Finite projective geometry
• mixed-level design
• minimum aberration
• secondary complementary set

2020 Mathematics Subject Classification:

• 62K15
• 62K05

Disclosure Statement

The authors declare there is no conflict of interest.

Acknowledgments

The authors thank the Associate Editor and two reviewers for their constructive comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11801308 and 12171277).