  We show that d+1-dimensional surface growth models can be mapped onto driven
lattice gases of d-mers. The continuous surface growth corresponds to one
dimensional drift of d-mers perpendicular to the (d-1)-dimensional "plane"
spanned by the d-mers. This facilitates efficient, bit-coded algorithms with
generalized Kawasaki dynamics of spins. Our simulations in d=2,3,4,5 dimensions
provide scaling exponent estimates on much larger system sizes and simulations
times published so far, where the effective growth exponent exhibits an
increase. We provide evidence for the agreement with field theoretical
predictions of the Kardar-Parisi-Zhang universality class and numerical
results. We show that the (2+1)-dimensional exponents conciliate with the
values suggested by Lassig within error margin, for the largest system sizes
studied here, but we can't support his predictions for (3+1)d numerically.
