We give a pseudorandom generator that fools m-facet polytopes over {0,1}^n with seed length polylog(m) * log(n). The previous best seed length had superlinear dependence on m. An immediate consequence is a deterministic quasipolynomial time algorithm for approximating the number of solutions to any {0,1}-integer program.

Joint work with Ryan O'Donnell and Rocco Servedio.