Vector assignment scheme for M+N users in N-dimensional global additive channel

N-dimensional global vector sets are constructed from the additive combinations of N+M individual N-dimensional vector sets. The minimum euclidean distance between vectors in the individual sets is maintained in the global set. The principal result is that users may be added to a Q-level system whenever N is a power of q² without decreasing the minimum distance. This finding may be applicable to synchronised multiuser communications.