Maskin (1999) proposes a well known monotonicity condition, which we refer to as Maskin monotonicity, and he shows it to be necessary and almost sufficient for Nash implementation. Although many implementation results using refinements of Nash equilibrium can dispense with Maskin monotonicity, a recent development in the literature shows that if we were to make implementation robust to information perturbations, Maskin monotonicity would come back as a necessary condition. Focusing on environments with lotteries and monetary transfers, we show that Maskin monotonicity is not only necessary but sufficient for robust implementation to information perturbations. To obtain this result, we construct a novel finite mechanism exploiting the notion of dictator lotteries of Abreu and Matsushima (1992) so that we fully characterize Nash implementation by finite mechanisms. Our mechanism possesses no obviously questionable features, handles the case of two agents, and takes care of mixed strategies explicitly. We extend Nash implementation result to the case of social choice correspondences. Finally, we also establish a full characterization of rationalizable implementation by finite mechanisms.