Before revision:  Notably, our dependence on n nearly matches the known upper bound  when \ell =  1  , and we reduce the dependence on \ell from doubly to nearly singly exponential.
After revision:  Notably, our dependence on n nearly matches the known upper bound DOS17, NP17 when \ell = 1 , and we reduce the dependence on \ell from doubly to nearly singly exponential.