  The deterministic capacity of a relay network is the capacity of a network
when relays are restricted to transmitting \emph{reliable} information, that
is, (asymptotically) deterministic function of the source message. In this
paper it is shown that the deterministic capacity of a number of MIMO relay
networks can be found in the low power regime where $\SNR\to0$. This is
accomplished through deriving single letter upper bounds and finding the limit
of these as $\SNR\to0$. The advantage of this technique is that it overcomes
the difficulty of finding optimum distributions for mutual information.
