Before revision: \] This exponentially improves  a recent result of Nederlof, Pawlewicz, Swennenhuis, and W\k{e}grzycki and leads to a similar improvement in the parameterized (by the number of bins) runtime of bin packing.
After revision: \] This exponentially improves the \epsilon dependence in a recent result of Nederlof, Pawlewicz, Swennenhuis, and W\k{e}grzycki and leads to a similar improvement in the parameterized (by the number of bins) runtime of bin packing.