 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.
<fluency>  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.
 Notably, our dependence on n nearly matches the known upper bound when \ell = 1 , and we reduce the dependence on \ell from doubly to singly exponential.