  We study the KPZ equation (in D = 2, 3 and 4 spatial dimensions) by using a
RSOS discretization of the surface. We measure the critical exponents very
precisely, and we show that the rational guess is not appropriate, and that 4D
is not the upper critical dimension. We are also able to determine very
precisely the exponent of the sub-leading scaling corrections, that turns out
to be close to 1 in all cases. We introduce and use a {\em multi-surface
coding} technique, that allow a gain of order 30 over usual numerical
simulations.
