Gus Method
Gus Method, or Grand Ultimate Supreme Method, is a method designed for quickly speedsolving the 3^4. The current speedsolving record of [7:43.33] by HactarCE is set using this method. The name Grand Ultimate Supreme comes from a modified version of the MC4D program that Luna made, which gets rid of some annoying keyboard shortcuts that have caused people to accidentally reset their log files.
Steps
4/6 Cross
Solve 4 out of the 6 cross pieces, with the cross colour being on the O cell. The unsolved cross spots will be on the Left and Right.
Belt F2L
Create and insert 4 F2L-a (2c3c) pairs into the 4/6 cross. This will solve 2/3 of the M slice. Because the Left and Right cells don't have their cross pieces, you can use them to aid with building and inserting the pairs.
Left
Solve the Left cell. Start with the cross piece, and then keep making pairs or building blocks to eventually complete the Left cell. The typical way this is done is by solving 3 2c3c pairs, then filling in the 2 3c4c pairs to complete a 2x2x3x1 block of the Left. Finally, the last 2c3c pair is inserted, followed by the last 2 3c4c pairs.
Another alternative approach is to do all the 2c3c pairs, followed by all the 3c4c pairs of the Left.
Right
Solve the Right cell. This will complete the First 2 Layers. Now that the Left cell is completed, you have more restrictions when making pairs. You can still do this step pretty much the same as the Left cell though. Keep making pairs or blocks and inserting them.
OLC
The last cell is oriented, as in Sheerin-Zhao Method. This is typically done by first orienting the 2c's, then 3c's, then 4c's, however the solver may wish to make use of setting up to big 3D OLLs, or use 4D specific algorithms if a case presents itself.
PLC
The last cell is permuted, as in Sheerin-Zhao Method. Do not forget to permute the 2c's first using EPLL algorithms. RKT is used to solve the last cell like a 3x3x3.