Suppose we consider 3-SAT with $v$ variables and $c$ clauses. I am researching a method that appears to take $O(v^{2+\log c})$ time/space to solve any SAT problem fitting this description, to within an error that can be adjusted to an arbitrary amount. However, there is a catch.
This method requires a set of precomputed values, after which it can solve an arbitrary 3-SAT problem fitting the above description. The precomputed values are a set of size $O(v^{2+\log c})$ with each value taking $O(1)$ space. The real problem is that each of these values could take $O(2^v)$ time to compute. There is a chance that I can find a way to speed up these calculations.
I'm thinking that the bounds itself beats the upper bounds presented in this question (for small $c$). So I'm wondering, is there a trivial way to reach the upper bounds I describe if we allow $O(v^{2+\log c})$ precomputations?
I'd like to continue this research and hopefully publish my results if everything works out, but first I'd like to know if there is a trivial way to do as well or better.
UPDATE
I have been studying related problems in addition to researching this algorithm. I asked This question on StackExchange's IT Security site relating to password cracking and SAT, if you are interested. At least one of the answers reflects this.