To estimate the coeffcients of the polynomial, the design matrix is expanded into a model matrix X that has an additional column which represents the constant term. The Plackett and Burman designs are only available for n 0 mod 4. Two approaches have been used to find saturated designs for the n 0 mod 4 cases. The Plackett and Burman designs are also related to BIB designs. For n 0 mod 4, the s ij cannot all be zero.
Some measure is needed to assess the effect of the nonorthogonality of the designs.
In the saturated case there are better measures of nonorthogonality. The VIF for b j is a factor indicating how much the variance of b j has been increased by the nonorthogonality of the design. To compute the effciency, the obtained quantity must be compared to that from the ideal design, which I consider to be an orthogonal design. Thus, these efficiencies are measures of deviation from orthogonality. For n 0 mod 4, optimal designs will have effciencies less than 1.