In this paper the functional correlation derived from the design matrix is introduced. It is shown how it can provide powerful insight into trade-offs in design. It also shows how the functional range is limited by functional correlation, and that this corresponds to a coupled design, although the converse is not true, i.e. a coupled design does not necessarily limit design space. In this way the functional correlation provides added insight into the design, compared to the design matrix. One important feature is that it is invariant to coordinate transformations of the design parameters. 

In this paper the notion of design information entropy with relation to a design space is also elaborated. It is shown that an uncoupled, and functionally uncorrelated design, corresponds to a minimization of waste of design space, and hence minimizes the information entropy needed to specify a design. In this paper it is also shown that this is directly related to the determinant of the design matrix.

A consequence, of the results in this study, is that the independence axiom and the information axiom, are not independent from each other, and although it is true that an uncoupled design also tend to minimize the information needed to specify a design, there are also coupled designs that also do so. It then follows that the overriding axiom is, that the best design space formulation is the one that minimize design information to specify a design.