Mike Reid:
> i've run an exhaustive search on the coset space G / H. the number
> of cosets at each distance is:

I can confirm Mike's results on phase 1. Here follows my table which
also contains the number of local maxima (which you will not find in
"backward" steps):

turns		 q	   loc.max	       q+h	   loc.max
    0	         1			         1
    1	         4			         4
    2	        34			        50
    3	       312			       592
    4	      2772			      7156
    5	     24996			     87236	         4
    6	    225949	         5	   1043817	        97
    7	   2017078	        32	  12070278	      2800
    8	  17554890	       730	 124946368	    110582
    9	 139132730	     39000	 821605960	  16713104
   10	 758147361	  10861351	1199128738	 750219596
   11	1182378518	 608836624	  58202444	  58196874
   12	 117594403	 117439129	       476	       476
   13	     14072	     14072

40 minutes for quarter turns, 47 minutes for face turns. this was done
on a DEC 3000 alpha 700, apparently a very fast machine.

I got 131 minutes for quarter turns and 186 minutes for face turns on a
measly SGI Challenge, apparently not so very fast. (I presume it would
have been faster if it had been possible to run with 64 bit long's.)

I will try to verify phase 2 later next week.

dik