Abstract: Strength three two-level orthogonal arrays with the number of runs equaling twice the number of factors are second-order saturated (SOS) designs. That is, for such designs one can construct a saturated model with an intercept, main effects, and two-factor interactions. Projections of this design onto subsets of factors provide no more degrees of freedom for two-factor interactions. This article explores the construction of other second-order saturated strength three arrays that allocate more than degrees of freedom for two-factor interactions. These new orthogonal arrays are constructed using two methods, one based on a foldover technique that reverses the signs of a subset of the columns of the strength three orthogonal array with , and the second based on the Kronecker product of an SOS design and a Hadamard matrix. We compare these new designs with respect to their generalized word length and alias length patterns.
Key words and phrases: Alias length pattern, complex aliasing, confounding frequency vector, doubling, foldover, nonregular design, resolution IV, two-factor interaction, word length pattern.