  In this paper we are concentrating on the diversity-multiplexing gain
trade-off (DMT) of some space-time lattice codes. First we give a DMT bound for
lattice codes having restricted dimension. We then recover the well known
results of the DMT of algebraic number field codes and the Alamouti code by
using the union bound and see that these codes do achieve the previously
mentioned bound. During our analysis interesting connections to the Dedekind's
zeta-function and to the unit group of algebraic number fields are revealed.
Finally we prove that both the number field codes and Alamouti code are in some
sense optimal codes in the multiple access channel (MAC).
