The D-optimal saturated designs of order 22

This paper attempts to prove the D-optimality of the saturated designs X* and X** of order 22, already existing in the current literature. The corresponding non-equivalent information matrices M*=(X*)X-T* and M**=(X**)X-T** have the maximum determinant. Within the application of a specific procedure, all symmetric and positive definite matrices M of order 22 with determinant the square of an integer and >= det(M*) are constructed. This procedure has indicated that there are 26 such non-equivalent matrices M, for 24 of which the non-existence of designs X such that (XX)-X-T=M is proved. The remaining two matrices M are the information matrices M* and M**. (C) 2017 Elsevier B.V. All rights reserved.