Projective Plane of Order 12 Objective: Settle the conjecture that there is no projective plane of order 12.

In 1989, using computer search on a Cray, Lam proved that no projective plane of order 10 exists.  Now that God's Number for Rubik's Cube has been determined after just a few weeks of massive brute force search (plus clever math of symmetry), it seems to me that this longstanding open problem might be within reach.  (Plus maybe we could use such techniques to solve something mathematically fundamental.)  I'm hoping this question can serve as a sanity check.

The Cube was solved by reducing the total problem size to "only" 2,217,093,120 distinct tests, which could be run in parallel.

Questions:


There have been several special cases of nonexistence shown.  Does anyone know, if we remove those and exhaustively search the rest, if the problem size is on the order of the Cube search?  (Maybe to much to hope for that someone knows this....)
Any partial information in this vein?


Edited to add: I asked this question on MathOverflow here.  So far it seems as though no search space reduction is achieved from the known partial results.  I still don't know the size of the total search space.
(More a comment than answer:)

Finite projective planes exist for values of n which are powers of a prime, and there are infinitely many values of n which are ruled out by a theorem of R.H. Bruck and H. Ryser, which was generalized to block designs by Chowla:

http://en.wikipedia.org/wiki/Bruck%E2%80%93Chowla%E2%80%93Ryser_theorem

n = 10, as was stated, was solved (no plane exists) by a computer search so the first value of n not ruled out by Bruck-Ryser is n = 12. However, the computer work did not seem to give new insights as to whether or not there are only the prime power planes. What seems to be needed are new mathematical methods for insight into the commonly made conjecture that only the prime power planes exist.