The depth-50 search completed yesterday, so the minimum length is now 51. Still running.

Here's a cute little algorithm that does it in 3150 moves (clearly not optimal):

(3u2 r 3u r 3u2 r' 3u' r 3u r)315
I have still not been able to beat the record 102 set by xyzzy. But I have found that there is no sequence shorter than 26 moves that when repeated 3 times is a pure double edge flip on UF.

I wrote a little routine in Mathematica earlier this year to find repeats of short sequences via a random scramble. (I did this to see if I could find alternate

short move sequences to repeat 5 times to get OLL parity.) I just adjusted it to the given constraints and it is giving me move sequences with a random number of required repeats.

Below are the shortest so far (I started with "depth"/Length 8).

*All of these flip a single dedge, but most do not flip the UF one. Ones which do flip the UF dedge have an * next to them. My program is finding one sequence every few seconds, on average.*
**Length of 8*** (All are 4,680 moves.)*
**(3Uw' Rw2 3Uw Rw 3Uw' Rw' 3Uw2 Rw)585**
(Rw' 3Uw2 Rw 3Uw Rw' 3Uw' Rw2 3Uw)585

(Rw 3Uw Rw2 3Uw' Rw 3Uw2 Rw' 3Uw')585

(Rw' 3Uw Rw2 3Uw' Rw' 3Uw Rw 3Uw2)585

(3Uw' Rw' 3Uw2 Rw 3Uw' Rw2 3Uw Rw)585

(Rw2 3Uw' Rw' 3Uw Rw 3Uw2 Rw' 3Uw)585

(Rw 3Uw Rw' 3Uw' Rw2 3Uw Rw' 3Uw2)585

(Rw 3Uw2 Rw' 3Uw' Rw 3Uw Rw2 3Uw')585

(Rw2 3Uw Rw' 3Uw2 Rw 3Uw Rw' 3Uw')585

(3Uw Rw2 3Uw' Rw 3Uw2 Rw' 3Uw' Rw)585

(3Uw Rw 3Uw' Rw' 3Uw2 Rw 3Uw' Rw2)585

(Rw2 3Uw Rw 3Uw' Rw' 3Uw2 Rw 3Uw')585

(3Uw2 Rw 3Uw Rw' 3Uw' Rw2 3Uw Rw')585

(3Uw2 Rw' 3Uw Rw2 3Uw' Rw' 3Uw Rw)585

(Rw 3Uw2 Rw' 3Uw Rw2 3Uw' Rw' 3Uw)585

(3Uw2 Rw 3Uw' Rw2 3Uw Rw 3Uw' Rw')585

(Rw2 3Uw' Rw 3Uw2 Rw' 3Uw' Rw 3Uw)585

(Rw 3Uw' Rw' 3Uw2 Rw 3Uw' Rw2 3Uw)585

(3Uw Rw' 3Uw2 Rw 3Uw Rw' 3Uw' Rw2)585

(Rw' 3Uw' Rw 3Uw Rw2 3Uw' Rw 3Uw2)585

(3Uw2 Rw' 3Uw' Rw 3Uw Rw2 3Uw' Rw)585

(3Uw' Rw' 3Uw Rw 3Uw2 Rw' 3Uw Rw2)585

(Rw' 3Uw Rw 3Uw2 Rw' 3Uw Rw2 3Uw')585

(3Uw' Rw2 3Uw Rw' 3Uw2 Rw 3Uw Rw')585

(3Uw' Rw 3Uw2 Rw' 3Uw' Rw 3Uw Rw2)585

**Length of 10 **(

*Tom, it also found the same sequence you posted which is of length 10, so I didn't include it*.)

*All of the following are obviously 150 moves.*
**(3Uw' Rw2 3Uw2 Rw2 3Uw2 Rw 3Uw2 Rw' 3Uw2 Rw)15**
(Rw' 3Uw2 Rw 3Uw2 Rw2 3Uw2 Rw2 3Uw' Rw 3Uw2)15

(Rw2 3Uw' Rw 3Uw2 Rw' 3Uw2 Rw 3Uw2 Rw2 3Uw2)15

(3Uw2 Rw' 3Uw2 Rw 3Uw2 Rw' 3Uw Rw2 3Uw2 Rw2)15

(3Uw2 Rw' 3Uw2 Rw2 3Uw2 Rw2 3Uw Rw' 3Uw2 Rw)15

(3Uw2 Rw' 3Uw2 Rw 3Uw' Rw2 3Uw2 Rw2 3Uw2 Rw)15

(3Uw2 Rw 3Uw2 Rw' 3Uw2 Rw2 3Uw2 Rw2 3Uw Rw')15

(3Uw2 Rw 3Uw2 Rw' 3Uw2 Rw 3Uw' Rw2 3Uw2 Rw2)15

(Rw' 3Uw2 Rw 3Uw' Rw2 3Uw2 Rw2 3Uw2 Rw 3Uw2)15

(Rw2 3Uw2 Rw2 3Uw2 Rw' 3Uw2 Rw 3Uw2 Rw' 3Uw)15

**(Rw' 3Uw' Rw' 3Uw2 Rw 3Uw Rw' 3Uw' Rw' 3Uw2)315** (3150 moves)*

**(Rw2 3Uw' Rw' 3Uw Rw' 3Uw' Rw2 3Uw2 Rw' 3Uw2)285** (2850 moves)

It seems that algorithms of Length 8 is the minimum, but I can't prove this. I am running my solver again to see if it finds any solutions which consist of repeating an algorithm 7 moves long. In addition, I may run it for Length 30 or so to see if I can beat xyzzy's alg length.