We give an explicit pseudorandom generator with seed length poly(log m, 1/\delta) * log n that \delta-fools the class of all m-facet polytopes over {0,1}^n. The previous best seed length had linear dependence on m. As a corollary, we obtain a deterministic quasipolynomial time algorithm for approximately counting the number of feasible solutions of general {0,1}-integer programs.