 Therefore, we are able to learn the mixture even for much larger values of \ell. For instance, Ban et . al.'s algorithm can only learn a mixture of O(\log n/\log \log n) strings with a subexponential number of queries, whereas we are able to learn a mixture of up to n^{o(1)} strings in subexponential queries\big(}\big)  and time.
<clarity>  Therefore, we are able to learn the mixture even for much larger values of \ell. For instance, Ban et . al.'s algorithm can only learn a mixture of O(\log n/\log \log n) strings with a subexponential number of queries, whereas we are able to learn a mixture of up to n^{o(1)} strings in subexponential queries\big(}\big)  and time.
 Therefore, we are able to learn large mixtures of strings: while Ban et al.'s algorithm can only learn a mixture of O(\log n/\log \log n) strings with a subexponential number of queries, whereas we are able to learn a mixture of up to n^{o(1)} strings in subexponential queries\big(}\big) and time.