Are quasi-polynomial sized circuits for 3-SAT trivial? 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.
If what you are studying worked out, it definitely would not be trivial.

It would imply that 3SAT has (non-uniform) circuits of size $n^{O(\log n)}$. Then, every language in $NP$ (and the polynomial time hierarchy) would have quasi-polynomial (i.e., $n^{O(\log^c n)}$) size circuits.

Even if it took $2^{2^n}$ preprocessing time to produce a data structure of size only $2^{O(\log^2 n)}$ which could then correctly answer arbitrary 3SAT queries of size $n$ in $2^{O(\log^2 n)}$ randomized time with high probability, 3SAT would have quasi-polynomial size circuits, using the known translation of randomized algorithms to circuits. This would not improve the known algorithm time bounds because of the preprocessing, but it would still be extremely interesting as a non-uniform result.

What do you mean by "to within an error that can be adjusted to an arbitrary amount"? Is the algorithm randomized?