I believe the idea is to provide an air space that a "fabric or screen" will be laid over.
I have used perlite.
Our local clime is important to note. You do see that there isn't any water drainage with Soma's design.
Roots that hit open air just stop growing. Roots that dry out die.
Roots grow to hold the plant up. The depth of soil determines the root space.
Try out a large plastic tub. Perhaps cut a drain hole in the side near the bottom. Place some perlite then some window screen fabric or other fabric over that. Cut two holes for air pipe. Fill with soil mix and try it.
I think that will be cheaper to test out for you than building a proper box.