Construction of three-level factorial designs with general minimum lower-order confounding via resolution IV designs

The general minimum lower order confounding (GMC) is a criterion for selecting designs when the experimenter has prior information about the order of the importance of the factors. The paper considers the construction of \(3^{n-m}\) $3^{n-m}$ designs under the GMC criterion. Based on some theoretical results, it proves that some large GMC \(3^{n-m}\) $3^{n-m}$ designs can be obtained by combining some small resolution IV designs T. All the results for \(4\le \#\{T\} \le 20\) $4\le \#\{T\}\le 20$ are tabulated in the table, where \(\#\) $\#$ means the cardinality of a set.