  We perform the Monte Carlo simulations of the hard-sphere lattice gas on the
simple cubic lattice with nearest neighbour exclusion. The critical activity is
estimated, $z_{\rm c} = 1.0588 \pm 0.0003$. Using a relation between the
hard-sphere lattice gas and the antiferromagnetic Ising model in an external
magnetic field, we conclude that there is no re-entrant phase transition of the
latter on the simple cubic lattice.
