  We apply a newly proposed Monte Carlo method, the Wang-Landau algorithm, to
the study of the three-dimensional antiferromagnetic q-state Potts models on a
simple cubic lattice. We systematically study the phase transition of the
models with q=3, 4, 5 and 6. We obtain the finite-temperature phase transition
for q= 3 and 4, whereas the transition temperature is down to zero for q=5. For
q=6 there exists no order for all the temperatures. We also study the
ground-state properties. The size-dependence of the ground-state entropy is
investigated. We find that the ground-state entropy is larger than the
contribution from the typical configurations of the broken-sublattice-symmetry
state for q=3. The same situations are found for q = 4, 5 and 6.
