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.
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. [Technical Report TR-CS-97-03, Department of Computer Science, Australian National University (1997).]