process. In particular it is not limited to linear coding or uncoded prefetching. This improved characterization is approximately a two-fold improvement with respect to the state of the art in current literature [@ghasemi15; @lim2016information].

Furthermore, for a practically important case where the number of files is large, we exactly characterize the rate-memory tradeoff for systems with no more than $5$ users. In this case, we also characterize the rate-memory tradeoff within a factor of $2$ for networks with an arbitrary number of users, slightly improving our factor-of-$2.00884$ characterization in the general case. In prior works, despite various attempts, this tradeoff has only been exactly characterized in two instances: the single-user case [@maddah-ali12a] and, more recently, the two-user case [@tian2016symmetry].

To prove these results we develop two new converse bounds for cache networks. The first converse is developed based on the idea of enhancing the cutset bound, to effectively capture the isolation of cache contents of the users that belong to the same side of the cut. This approach strictly improves the compound cutset bound, which was used in most of the prior works. Furthermore, using this converse, we are able to characterize both the peak rate and the average rate 