A-optimization of exact first-order saturated designs for N ≡ 1 mod 4 observations Original Research Article

The case of exact first-order saturated designs with N ≡ 1 mod 4 observations [N ≠ 2s(s + 1) + 1, S = 1,2,…] is considered. Conditions are found for the A-optimality of such designs, when the first r rows of the corresponding design matrix have a known structure. By modifying the method of Sathe and Shenoy (1989) for the case N ≡ 1 mod 4, the structure of the information matrix of the A-optimal design is found. Then, by exhaustive search, it is proved that the known D-optimal saturated design for N = 9 (Ehlich, 1964) is also A-optimal.