Balanced fractional \(r^m\times s^n\) factorial designs and their analysis (Q1158712)

This longish paper (after the reader has digested quite a bit of notation and algebra) presents results on fractional factorial designs of the \(r^m\times s^n\) type. Results on orthogonal and balenced fractional factorial designs (with most of the attention focused on odd-resolution types) are obtained using notions of asymmetrical orthogonal array, asymmetrical balanced arrays and multidimensional relationships. Determinant and trace optimal construction aspects are illustrated for the \(2^2\times 3^2\) balanced fractional factorial designs of resolution \(V\).