  We study the Restricted Solid on Solid (RSOS) model for surface growth in
spatial dimension d=4 by means of a multi-surface coding technique that allows
to analyze samples to analyze samples of size up to $256^4$ in the steady state
regime. For such large systems we are able to achieve a controlled asymptotic
regime where the typical scale of the fluctuations are larger than the lattice
spacing used in the simulations. A careful finite-size scaling analysis of the
critical exponents clearly indicate that d=4 is not the upper critical
dimension of the model.
