The third order design (THOD) has been defined as the problem of improving, extending or densifying an existing network in an optimal way by introducing additional points and/or additional observations. Two generally different problems are coming up in the THOD: The one is the optimal improvement of the network the other is the optimal design of a densification network. Both tasks are in principal mixed first and second order design problems, because changes in the point location as well as changes in the elements of the observation plan and changes in the precision of the observations can be treated. In the design ordering we characterized this fact by stating that the configuration matrix A and the weight matrix P are partly free.