Abstract An orthogonal polynomial model is used to model the response influenced by n two level factors. Such a model is represented by an undirected graph g with n vertices and e edges. The vertices identify the n main effects and the e edges identify the two-factor interactions of interest which together with the mean are the parameters of interest. A g -design is a saturated design which can provide an unbiased estimator for these parameters and its design matrix is called a g -matrix. The latter two concepts were introduced by Hedayat and Pesotan (Statistica Sinica 2 (1992), 453–464). In this paper methods of constructing g -matrices are studied since such constructions are equivalent to the construction of g -designs. Some bounds on the absolute value of a determinant of a g -matrix are given and D-optimality results on certain classes of g -matrices are presented.
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