We give a pseudorandom generator that fools $m$-facet polytopes over ${0,1}^n$ with seed length $mathrm{polylog}(m) cdot log n$. 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.
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