My Lauter Tun is a ten gallon Rubbermaid cooler. I first set it up with a 12 inch domed false bottom. I used it a few times, but was not please with the fact that eventually I got grain into my boil kettle through the false bottom. I thought that some of this was due to my false bottom not sitting tightly against the cooler floor, allowing grain to pass between the cooler floor and the false bottom.
So, I purchased a hot water supply line from HD, and salvaged the stainless sheath from that. I fashioned a loop out of this using a 5/8 brass fitting with compression fittings. This allows the braid to loop around, and allows for it to fasten into my bulkhead fitting. (I used John Palmer's book for exact details). I loved how this was working for me. No more grain in my boil kettle.
Then about a year ago, I refashioned my MLT to accept a Bayou Classic 11 gallon pot that I fit inside my Rubbermaid cooler (ala Ben's Build for New Mash Tun
here). I decided to give the false bottom a try again with the new mash tun (I figured that the plastic warped causing the gap, and the stainless steel would provide a better fit). I used the false bottom for a couple of batches, and did not like the way it worked. I soon went back to my stainless braid.
I know some people have great success with the false bottom, but my experience is that the braid works much better. Also, I have done nothing but batch sparge, if this makes a difference.)
I hope that this helps.
Mark