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I found/genned/used these algs:
B' U2 r' U r U2 B
F R2 U R U' R2 F'
R U2 F R F' U2 R'
F D U R' U' R D' F'
U B R' U' R U l U' l'
U' F R2 U R' U' R2 F'
R U R U R U' R' U' R'
U' R U R U R2 U' R' U' R'
U2 R U R U R' U' R' U' R'
R U R' D R2 U' R U R2 D'
U' R' F R' F' R2 U2 R' U' R
D' R U R' D R2 U' R U R2
R2 U' R2 U' R' U R' U R2

Hey guys, a while ago I asked the community what they thought the best OLL case for ZBLL was and top 3 (before the poll was taken down) were U, L, and in first was T. So, I genned to a depth 11 the connected pair to always force a T ZBLL.
P.S I didn't include AUF's just saying that now rather than later.

I generatad more algs for this case
Setup: F U R U2 R' U R U R' U R U2 R' U R U R' F'
And although the standard which is the inverse of that setup is good and the #1 on algdb I don't like it so I generated some more algs and these are the best I have currently:

F R U' R' U' R U2 R' U' R U' R' U' R U2 R' U' F'
F U2 R U' R' U2 R2 U2 R2 U' R2 U' R' U' R' F'
F R U R U R2 U R2 U2 R2 U2 R U R' U2 F'
F R2 U2 R2 U' R2 U' R' U' R' U2 R U' R' U2 F'
F U R U2 R' U R U R' U R U2 R' U R U R' F'
U R2 L' U R U' R' L U R U R2 U' R2 U2 R U' R'
R U R2 U' R U R2 U2 R2 U2 R U2 D' R U R' D R

If anyone has an alg they think is awesome but is not on this let please let me know.

I generatad more algs for this case
Setup: F U R U2 R' U R U R' U R U2 R' U R U R' F'
And although the standard which is the inverse of that setup is good and the #1 on algdb I don't like it so I generated some more algs and these are the best I have currently:

F R U' R' U' R U2 R' U' R U' R' U' R U2 R' U' F'
F U2 R U' R' U2 R2 U2 R2 U' R2 U' R' U' R' F'
F R U R U R2 U R2 U2 R2 U2 R U R' U2 F'
F R2 U2 R2 U' R2 U' R' U' R' U2 R U' R' U2 F'
F U R U2 R' U R U R' U R U2 R' U R U R' F'
U R2 L' U R U' R' L U R U R2 U' R2 U2 R U' R'
R U R2 U' R U R2 U2 R2 U2 R U2 D' R U R' D R

If anyone has an alg they think is awesome but is not on this let please let me know.

I've seen something like (y2) F U2 R2 U2 R2 U' S R2 S' U' R2 F' before, which is cool to execute but not exactly fast due to all the wrist turning and overworking. I personally use the first alg in your list.

Hey guys check out this alg I genned and got a sub 2 with it last night. Case is ZBLL Pi 17
R' U' R U R2 F' R U R U' R' F U' R U R' U R
I think it's a fun and fast alg.

Does anyone here have fast algorithms for OLL (specifically L, U, and T cases) which permute edges?

Assume edges are all correctly oriented and I would like to keep them that way.

I am trying to come up with an algorithm set that allows me to phase edges while solving OLL, and it is surprisingly hard to find the above algorithms.

Does anyone here have fast algorithms for OLL (specifically L, U, and T cases) which permute edges?

Assume edges are all correctly oriented and I would like to keep them that way.

I am trying to come up with an algorithm set that allows me to phase edges while solving OLL, and it is surprisingly hard to find the above algorithms.

Just phasing them so that they are either solved or have parity.

To lessen my possible PLL cases. Yes, I am aware that unphased PLL algs are generally faster (e.g., U perm vs. Z perm). This is simply for convenience for a beginner like myself.

Basically for each OLL case with correctly oriented edges, I have 3 algs. One which permutes edges clockwise while solving OLL, one which permutes CCW, and one which preserves edges (i.e., OCLL).

Does anyone here have fast algorithms for OLL (specifically L, U, and T cases) which permute edges?

Assume edges are all correctly oriented and I would like to keep them that way.

I am trying to come up with an algorithm set that allows me to phase edges while solving OLL, and it is surprisingly hard to find the above algorithms.

T (oriented corners on right):
F/B: r U R' U' r' F R F'
F/L: R U2 R' U2 R' F R U R U' R' F' or (U2) F U R U2 R' U R U R' F'
F/R: (U') D R' U' R U D' R U' R U R U' R2 or (U') L' U R' U' L R U2 R' U' R

U (oriented corners in front):
F/B: R2 D' R U2 R' D R U2 R
F/L: R2 D' r U2 r' D R U2 R or R' U2 R F U' R' U' R U F'
F/R: (U2) R2 D r' U2 r D' R' U2 R' or (U') F U' R' U R U F' R' U2 R

L (LL colour facing you on FUR corner):
F/B: F' r U R' U' r' F R or R2 D R' U R D' R' U' R'
F/L: (U') r U2 R2 F R F' R U2 r'
F/R: (U') F R U' R' U' R U2 R' U' F'