I have the net pots 2" and am making a floating raft bed out of 1 1/2 inch Dow BlueBoard. What size hole saw do I need. The net pots are the ones shown in the link.
I have looked online for a 1 7/8" hole saw which I think would work but haven't been able to find one that won't tear-up the foamboard and is deep enough.
When I've drilled holes through thicker foam, I found I needed to start the whole on one side and then flip the board over to finish the whole from the other side. Might require a longer bit to create the pilot hole all the way through before you start so that you will be able to line it up when you flip it over.
I've done holes through such board using regular old hole saws for wood. The biggest challenge with the net pots is you don't have very much lip to hold the pot on the surface (I used yogurt cups that had the nice big rim and I didn't need the holes to be perfect in order to hold the cups.)
Some people have recommended to run the drill backwards as you do the hole saw through the foam, I'm not sure how well this works but maybe it won't tear up the foam so bad? Make sure to do it in a well ventilated area since you will likely be burning the hole through the foam more than cutting it that way.
I'd take the net pot in to the hardware store with you and see if a clerk will open a hole saw kit and let you check sizes. You definitely want the outside of the hole saw to be smaller than the rim of your net pot, perhaps even hold the net pot up so the rim doesn't even rest on the surface, that way you will get some wear out of it before the net pots are likely to start trying to fall through the foam.