What size piping a more detailed question ?

I have an external pump that is rated at 3800 gph what size pipe should I
use? My pump actually moves around 1800 GPH currently and forms a suction on
the 2" inlet pipe. My pump, has a 4' tall p-trap, that has a 2" intake that
is located 6" below the water line and can not run with the top off the Pump
Trap. The pump will drain the canister dry. I imagine this is causing the
flow to be restricted also. I am going to but a larger hole in the liner and
put a 3" pipe in then reduce to 2" pipe right before the canister and hope
this helps with the flow. Water only fills about a quarter of the pipe
running into the p-trap when it flow naturally". I am thinking of moving the
hole down further in the liner say 12" to help fill the canister up faster.
I think the canister should be filled up so fast I have to keep the cap on
to keep water from the pond from overflowing not to keep the canister from
running dry.