Re-read my post - the whole point is not to store the powerset anywhere. A set with only 100 elements in my scheme needs to be stored only once. That's 13 bytes in a bit vector. The powerset is implied by checking against subsets of it using bitwise & operations.
The problem is when there are multiple sets, there are multiple checks. 500 sets of 100 elements each only require 6.5k to store in memory, but require up to 500 checks to determine if the set I'm currently working with is a subset of any of them. It's that searching through those sets I want to speed up.