From any ZBLL we can easily get to PLL using only 2gen moves. All PLLs are a U, Z, or H perm away from either solved, R perm, or Y perm. Therefore, if we can do R and Y perm with at most 2 D-layer moves, we can do any ZBLL with at most 2 D-layer moves.
So, here is an R perm with exactly 2 D-layer moves:
R U2 R D R' U R D' R' U' R' U R U R' U
And here is a Y perm (but not an efficient one):
R' U' D (R' U' R U)3 D' U R (R U R' U R U2 R')2 U'
I imagine these algs could be very useful for OH - everyone loves 2gen moves, and keeping D turns to a minimum is very helpful. Unfortunately, I don't know of any way to generate optimal algs of this type. Does anyone have an idea?
P.S. You can also do every ZBLL with
F (R U R' U')3 F' U (R U R' U R U2 R')2 U2
From http://www.speedsolving.com/forum/showthread.php?708&p=680961#post680961 (December 2011):
Dumping some optimal 2-F-move PLLs (there are probably a few optimal ones I missed but the optimal lengths should be accurate):
A-perm a HTM-optimal: 11f R U' R F2 R' U R' U' R2 F2 R2 QTM-optimal: 15q R U' R F2 R' U R' U' R2 F2 R2 A-perm a HTM-optimal: 11f R2 F2 R2 U R U' R F2 R' U R' QTM-optimal: 15q R2 F2 R2 U R U' R F2 R' U R'
E-perm
HTM-optimal: 18f R' U2 R U' F' R' U R' U2 R U R' U R2 F R' U' R R' U R F' R2 U' R U' R' U2 R U' R F U R' U2 R R U R' U R' F U' R2 U' R2 U2 R' U' R F' R' U R2 R2 U F' U R' U' R U R' U' R U R' U' R F U' R2 R2 U F' R' U R U' R' U R U' R' U R U' F U' R2 R2 U' R F R' U R U2 R2 U R2 U F' R U' R U' R' R2 U2 F' U' R' U R U' R' U R U' R' U R F U2 R2 R2 U2 F' R' U' R U R' U' R U R' U' R U F U2 R2 F U R2 U' R U R' U R2 U' R' U R' U' R U' R F' F U' R U' R U R' U R U2 R' U R' U' R U2 R' F' F U' R U' R' U2 R U' R' U R' U2 R U R' U R F' F U' R' U R' U' R2 U R' U R U' R2 U R U' R F' F R U2 R' U R U' R U2 R' U' R U' R' U R' U F' F R' U R' U R U' R U R2 U' R U' R' U R2 U' F' F R' U R' U' R2 U R' U' R U' R2 U R U' R U F' F R' U' R U' R' U2 R U' R U R' U2 R U R' U F' QTM-optimal: 20q R2 U F' U R' U' R U R' U' R U R' U' R F U' R2 R2 U F' R' U R U' R' U R U' R' U R U' F U' R2 F U R2 U' R U R' U R2 U' R' U R' U' R U' R F' F U' R U' R U R' U R U2 R' U R' U' R U2 R' F' F U' R U' R' U2 R U' R' U R' U2 R U R' U R F' F U' R' U R' U' R2 U R' U R U' R2 U R U' R F' F R U2 R' U R U' R U2 R' U' R U' R' U R' U F' F R' U R' U R U' R U R2 U' R U' R' U R2 U' F' F R' U R' U' R2 U R' U' R U' R2 U R U' R U F' F R' U' R U' R' U2 R U' R U R' U2 R U R' U F'
F-perm HTM-optimal: 15f R2 U R2 U2 F2 U R2 U2 R2 U R2 U' R2 U2 F2 R2 U R2 U' R2 U2 R2 U' F2 U2 R2 U' R2 U' F2 F2 U R2 U R2 U2 F2 U R2 U2 R2 U R2 U' R2 F2 U2 R2 U R2 U' R2 U2 R2 U' F2 U2 R2 U' R2 R2 U' F2 U2 R2 U' R2 U2 R2 U R2 U F2 U2 R2 R2 U2 F2 U' R2 U' R2 U2 R2 U R2 U2 F2 U R2 QTM-optimal: 19q R U R' U' R' U R U F' U R' U R U2 F R U' R' R U R' F' U2 R' U' R U' F U' R' U' R U R U' R' R U R U F' U' R U R' U' R' U2 F U' R' U2 R' R U2 R U F' U2 R U R U' R' U F U' R' U' R' R' U' R U' R' U R U R2 F' R U R U' R' F U R R' U' F' R U R' U' R' F R2 U' R' U' R U R' U R
G-perm a HTM-optimal: 15f F2 U R U2 R' U' R' U2 R2 U R' F2 R' U R R' U' F2 U R U2 R U2 R' U F2 U2 R U' R' QTM-optimal: 18q R U R' U' R' U F R U R U' R' F' U R' U2 R
G-perm b HTM-optimal: 15f R' U' R F2 R U' R2 U2 R U R U2 R' U' F2 R U R' U2 F2 U' R U2 R' U2 R' U' F2 U R QTM-optimal: 18q R' U2 R U' F R U R' U' R' F' U' R U R U' R'
G-perm c
HTM-optimal: 14f R2 U2 R2 F2 U' R2 U R2 U F2 U2 R2 U' R2 QTM-optimal: 17q R2 U' R U' R U R' U R' F' R' U R U' F R'
G-perm d HTM-optimal: 14f R2 U R2 U2 F2 U' R2 U' R2 U F2 R2 U2 R2 QTM-optimal: 17q R F' U R' U' R F R U' R U' R' U R' U R2
J-perm a HTM-optimal: 13f R' F R' U' R2 U' R2 U R' F' R U R2 R2 U' R' F R U' R2 U R2 U R F' R QTM-optimal: 16q R' F R' U' R2 U' R2 U R' F' R U R2 R2 U' R' F R U' R2 U R2 U R F' R F R' U R U' F' U R' U2 R U' R' U2 R R' U2 R U R' U2 R U' F U R' U' R F' R' U' R U F R U' R' U' R' U R2 U R' F' R' U' R U' R' U F U R' U' R F' R' U R2 R2 U' R F R' U R U' F' U' R U R' U R F R U' R2 U' R U R U R' F' U' R' U R
J-perm b HTM-optimal: 11f R U' F U' R' U' R U F' U2 R' R U2 F U' R' U R U F' U R' QTM-optimal: 12q R U' F U' R' U' R U F' U2 R' R U2 F U' R' U R U F' U R'
N-perm a HTM-optimal: 15f R2 U R2 U' R2 U' F2 U' R2 U R2 U F2 U2 R2 R2 U2 F2 U' R2 U' R2 U F2 U R2 U R2 U' R2 QTM-optimal: 21q R U2 R2 U' R2 F' R U R' U' R' F R' U R U2 R' R U2 R' U' R F' R U R U' R' F R2 U R2 U2 R' R U R' U R U' F U' R' U' R U F' U2 R' U2 R U' R' R U R' U2 R U2 F U' R' U R U F' U R' U' R U' R'
N-perm b HTM-optimal: 15f R2 U F2 U2 R2 U R2 U2 R2 U' R2 U2 F2 U' R2 R2 U' R2 U2 F2 U' R2 U2 R2 U F2 U2 R2 U R2 QTM-optimal: 23q? R U' R' U R' U2 R2 U R2 F2 U R U R U' R' U' F2 F2 U R U R' U' R' U' F2 R2 U' R2 U2 R U' R U R' R' U2 R' U' R2 U F' U' R U R' U' R2 U2 R F R' U R R' U2 F U R2 U2 R' U' R U R' F' R U2 R' U' R' U R R' U' R U R U2 R' F R U' R' U R U2 R2 U' F' U2 R R' U' R F' R' U2 R2 U R U' R' U F U' R2 U R U2 R
R-perm a HTM-optimal: 13f R2 F2 U R U R' U' R' U' F2 R' U R' R U' R F2 U R U R U' R' U' F2 R2 QTM-optimal: 16q R2 F2 U R U R' U' R' U' F2 R' U R' R U' R F2 U R U R U' R' U' F2 R2
R-perm b
HTM-optimal: 13f R2 F R U R U' R' F' R U2 R' U2 R R' U2 R U2 R' F R U R' U' R' F' R2 QTM-optimal: 16q R2 F R U R U' R' F' R U2 R' U2 R R' U2 R U2 R' F R U R' U' R' F' R2
T-perm
HTM-optimal: 14f R U R' U' R' F R2 U' R' U' R U R' F' F R U' R' U R U R2 F' R U R U' R' QTM-optimal: 15q R U R' U' R' F R2 U' R' U' R U R' F' F R U' R' U R U R2 F' R U R U' R'
V-perm HTM-optimal: 15f R2 U2 R2 U R2 U2 F2 U R2 U R2 U2 F2 U' R2 R2 U2 R2 U' F2 U2 R2 U' R2 U' F2 U2 R2 U R2 R2 U F2 U2 R2 U' R2 U' F2 U2 R2 U' R2 U2 R2 R2 U' R2 U2 F2 U R2 U R2 U2 F2 U R2 U2 R2 QTM-optimal: 19q R U' R' U R F R' U' R2 U R U' R U R2 F' R' R F R2 U' R' U R' U' R2 U R F' R' U' R U R'
Y-perm
HTM-optimal: 14f R2 U' R2 U F2 U' R2 U' R2 U F2 R2 U R2 R2 U' R2 F2 U' R2 U R2 U F2 U' R2 U R2 QTM-optimal: 19q R2 U' R2 U' R2 U R' F' R U R2 U' R' F R R' F' R U R2 U' R' F R U' R2 U R2 U R2 R' U' R U' R U' F U' R' U' R U F' U2 R2 U R R' U' R2 U2 F U' R' U R U F' U R' U R' U R
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