Before revision:  We also give the first algorithm with a runtime subexponential in n, which solves population recovery in \exp\big(\tilde{O}(n^{1/3}) \cdot \ell^3\big) samples and time.
After revision:  We also give the first algorithm with a runtime subexponential in n, solving population recovery in \exp\big(\tilde{O}(n^{1/3}) \cdot \ell^3\big) samples and time.