Construction of 2ᵐ4ⁿ Designs via a Grouping Scheme

We develop a method for grouping the 2ᵏ - 1 factorial effects in a 2-level factorial design into mutually exclusive sets of the form $(s, t, st)$, where $st$ is the generalized interaction of effects s and t. As an application, we construct orthogonal arrays OA(2ᵏ, 2ᵐ4ⁿ, 2) of size 2ᵏ, m constraints with 2 levels and n constraints with 4 levels in the construction cannot be further improved. In this sense our grouping scheme is optimal. We discuss the advantages of the present approach over other construction methods.