[en] In this work, the authors discuss the results of extensive numerical simulations in order to estimate the scaling exponents associated with kinetic roughening in higher dimensions, up to d = 7+1. To this end, they study the restricted solid-on-solid growth model, for which a novel fitting ansatz is employed for the spatially averaged height correlation function G(t) ∼t^2β to estimate the scaling exponent β. Using this method, a quantitative determination is presented of β in d = 3+1 and 4+1 dimensions. To check the consistency of these results, the authors also compute the interface width and determine β and χ from it independently. These results are in disagreement with all existing theories and conjectures, but in four dimensions they are in good agreement with recent simulations of Forrest and Tang for a different growth model. Above five dimensions, the time dependence of the width can be used to obtain lower bound estimates for β. Within the accuracy of our data, no indication is found of an upper critical dimension up to d = 7+1. 28 refs., 9 figs