i've finished searching for superflip in 20q , and no solutions were
found. thus superflip requires at least 22q , which gives a new lower
bound for the diameter of the cube group in the quarter turn metric.
total cpu spent on the search was 29 cpu hours. based on this, i would
make a rough estimate of 2.5 to 3 months cpu time for an exhaustive
search through depth 22q.

this time i collected some statistics the way dik did. this should be
helpful for troubleshooting. it's not foolproof, but it's a reasonable
start. i will rerun the face turn search and collect the same data
along the way.

mike

statistics follow:

depth in        number of times          solutions
stage 1        stage 2 is reached          found

superflip  R1 L1 U1:

 9q                     64               33q, 31q, 29q
10q                    272
11q                   3728               27q
12q                  26440
13q                 164664               25q
14q                 911112
15q                5516208
 
superflip  R1 L1 U3:

 9q                     64               31q, 29q, 27q
10q                    272
11q                   3728
12q                  26440
13q                 164664
14q                 911112               25q
15q                5516208

superflip  R1 L1 F1:

 9q                    288               31q, 29q, 27q
10q                   2192
11q                  13496
12q                  65280
13q                 352056               25q, 23q
14q                1810744
15q                9753608

superflip  R1 L1 F3:

 9q                    288               31q, 29q, 27q
10q                   2192
11q                  13496
12q                  65280               25q
13q                 352056
14q                1810744
15q                9753608

superflip  R1 L3 U1:

 9q                     64               33q, 31q, 29q, 27q
10q                    272
11q                   3728
12q                  26440               25q
13q                 164664
14q                 911112               23q
15q                5516208

superflip  R1 L3 F1:

 9q                    288               33q, 31q, 29q
10q                   2192               27q
11q                  13496               25q
12q                  65280
13q                 352056
14q                1810744
15q                9753608

superflip R1 U1:

10q                      6               32q
11q                    106               28q
12q                   4216               26q
13q                  30318
14q                 212208
15q                1414882
16q                9807890

superflip R1 U3:

10q                      6               32q
11q                    106               30q, 28q
12q                   4216               26q
13q                  30318
14q                 212208               24q
15q                1414882
16q                9807890

superflip R1 F1:

10q                     78               32q, 30q, 28q
11q                    352
12q                   5338               26q, 24q
13q                  35996
14q                 241230
15q                1549382
16q               10531798
17q               71358512

superflip R1 F3:

10q                     78               28q
11q                    352
12q                   5338               26q, 24q
13q                  35996
14q                 241230
15q                1549382
16q               10531798
17q               71358512