#P is the class of counting problems for problems in NP. In other words, a solution to #P returns the number of solutions to a particular problem in NP.
I'm wondering if there have been any studies on the worst-case behaviors of current best solutions to problems in NP. My focus in the past has been on 3-SAT, so I am particularly interested in the time it takes to count 3-SAT solutions in the worst case. However, I ask in general, What are the current best upper bounds for any (#P-complete) problem in #P?