Gunno Toernberg tells me he has been working on a computer approach to the problem: you can see his endeavours at: http://w1.859.telia.com/~u85905224/knight/eknight.htm where you can have ago on his Java board.
Comments on: Martin Loebbing and Ingo Wegener, The Number of Knight's Tours Equals 33,439,123,484,294 --- Counting with Binary Decision Diagrams Comment by the authors, May 15, 1996: The number of knight's tours given in the paper is incorrect, since the correct number must be divisible by 4. The method and the running time are correct. We will re-run the computations, which involves the use of many computers, and announce the results here when they are available. Comment from Brendan McKay, Feb 18, 1997: I have recomputed the number of knight's tours using another method, and obtained the answer 13,267,364,410,532. A description is available in PostScript. [Technical Report TR-CS-97-03, Department of Computer Science, Australian National University (1997).]