In Gentry's seminal paper on fully homomorphic encryption (FHE), it is assumed that the sparse subset set problem is hard. It looks like there is a followup paper on the concrete parameter of the subset size, which mentions that Gentry's choice of subset size is too aggressive (e.g., 15). However, in its section 5 (Discussion), it also mentioned that the real assumption used Gentry's paper is the hidden sparse subset problem and its analysis does not apply.
So, regarding the choice of subset size, what is regarded as a "safe" parameter for the hidden sparse subset problem right now? E.g., given the size of the entire set of weights be 32k used in Gentry's paper?