  We study the 3D Disordered Potts Model with p=5 and p=6. Our numerical
simulations (that severely slow down for increasing p) detect a very clear spin
glass phase transition. We evaluate the critical exponents and the critical
value of the temperature, and we use known results at lower $p$ values to
discuss how they evolve for increasing p. We do not find any sign of the
presence of a transition to a ferromagnetic regime.
