  For all $n, \epsilon >0$, we show that the set of Poisson Binomial
distributions on $n$ variables admits a proper $\epsilon$-cover in total
variation distance of size $n^2+n \cdot (1/\epsilon)^{O(\log^2 (1/\epsilon))}$,
which can also be computed in polynomial time. We discuss the implications of
our construction for approximation algorithms and the computation of
approximate Nash equilibria in anonymous games.
