Optimal fractional factorial designs for estimating interactions of one factor with all others: 3m Series

In some experimental situations, only one factor is expected to interact with other factors. Designs which permit estimation of all main effects and the interactions of one factor ‘With All Others’, are termed WAO designs. This paper discusses the existence and construction of s^m WAO designs. A series of WAO designs are presented for the 3^m factorial, for m = 6, 7, ... , 14. The p non-negligible effects are estimable in 9f^? runs, where f^? is the smallest integer such that 9f^? ≥p. These designs are determinant optimal within the class of parallel flats fractions and, except for the case f^? = 9, are new. They are ideally suited for sequential experiments.