  The mapping class group of a Heegaard splitting is the group of connected
components in the set of automorphisms of the ambient manifold that map the
Heegaard surface onto itself. For the genus three Heegaard splitting of the
3-torus, we find an eight element generating set for this group. Six of these
generators induce generating elements of the mapping class group of the 3-torus
and the remaining two are isotopy trivial in the 3-torus.
