  We establish several new topological generation results for the quantum
permutation groups $S^+_N$ and the quantum reflection groups $H^{s+}_N$. We use
these results to show that these quantum groups admit sufficiently many "matrix
models". In particular, all of these quantum groups have residually finite
discrete duals (and are, in particular, hyperlinear), and certain "flat" matrix
models for $S_N^+$ are inner faithful.
