Some results on $2^{n-m}$ designs of resolution IV with (weak) minimum aberration

TL;DR

This paper explores the structure of resolution IV $2^{n-m}$ designs, establishing relationships between their wordlength patterns and complements, and constructs several families of designs with minimal aberration.

Contribution

It derives explicit formulas linking wordlength patterns of even $2^{n-m}$ designs and their complements, enabling the construction of minimum aberration designs.

Findings

Identified relationships between design and complement wordlength patterns.

Constructed new families of minimum aberration $2^{n-m}$ designs.

Characterized structures of complementary designs.

Abstract

It is known that all resolution IV regular $2^{n-m}$ designs of run size $N=2^{n-m}$ where $5N/16<n<N/2$ must be projections of the maximal even design with $N/2$ factors and, therefore, are even designs. This paper derives a general and explicit relationship between the wordlength pattern of any even $2^{n-m}$ design and that of its complement in the maximal even design. Using these identities, we identify some (weak) minimum aberration $2^{n-m}$ designs of resolution IV and the structures of their complementary designs. Based on these results, several families of minimum aberration $2^{n-m}$ designs of resolution IV are constructed.