From:

Subject:

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