  We calculate rigorous lower bounds for the ground state degeneracy per site,
$W$, of the $q$-state Potts antiferromagnet on slabs of the simple cubic
lattice that are infinite in two directions and finite in the third and that
thus interpolate between the square (sq) and simple cubic (sc) lattices. We
give a comparison with large-$q$ series expansions for the sq and sc lattices
and also present numerical comparisons.
