What you need for P strips depends on how you connected the S strips, and how much current you will ever *actually* draw (not just what cells are capable of).
If you have S connections across the *entire* current path from every P cell to the next S group of P cells, then the P strips don't carry the current, just the S strips do.
If you use only certain points to make S connections, then the P strips have to carry the current from the non-S connected cells to that point, and so the P strips have to be capable of whatever that current is.
Example:
Let's say you will have an absolute max of 60A ever drawn from the pack by the system (60A current limit in the controller).
Let's say you have a P strip across each row of 6 cells.
Let's say you have two S strips from about the middle of each 3 cells in those over to the next S row of cells.
Those S strips have to then handle *at least* 30A each.
The P strips have to handle *at least* however much current flows from the two cells on either side of the S strip connections, assuming perfect current distribution that should be 10A...but it probably won't be perfect as cells and interconnect resistances vary, so actual loads will vary with them, making it better to up that by at least whatever percentage those will vary.
Let's say you have the same setup, but with S-strips that go from straight from each cell in one P group to the corresponding cell in the next S'd P group.
Now all the current from each cell will flow right thru that S strip and not have to go thru the P strip at all. The P strips are "backups" in case of an S strip interconnect failure, and to connect all the P group cells together to enable/ensure balancing / enable cell-group monitoring.
Let's say you have a non-rectangular layout, where some groups connect to the next with different widths of S connection (different numbers of S strips, etc). Now you have to use thicker strips on some than others, both for P and S, depending on which ones are connected in what physical arrangements.
So...it depends on how you physically build your pack.