In Germany wd have for this a rule of thumb. If it's possible to work with an sump or large filter on an pond the prefered size would be 10% net volume of the main tank.
So 125 Gallons ÷ 10 = 12.5 Gallons of Media.
This rule is taken out of the koi breeding szene where we have far higher bioloads so with that you can drive basicly any avaible fish for the tank size.
That would be at least the number you should have as a bare minimum. Now it depends what kind of sump you wanna run. Than some types don't allow fillings above 1/4 of the tank volume like bucky shower towers.
Submerged chamber sump
All have there advantages and disadvantages. For example moving bed is a good System if it's once cycled but it's very loud if not propper isolated and if the airpump is not in another room.
We need to stop talking about the people as if they were the crown of creation.
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