I built one for my kids and one for a nephew. I ordered the 10" x 10" Lego plates from Amazon. The sides and top are made from 3/4" plywood and the bottom is 1/4" plywood. The overall dimensions are 26 1/4" x 13 5/8" x 11 7/8" (not counting the top circles). I used a 4" hole saw to cut the circles then glued/nailed two together and used wood filler to fill the hole created in the center of the circles by the hole saw.
Other than changing the dimensions, I followed the original plans closely. The images in the original plans have 2 plates that are 15" x 15".
When cutting the circles, I clamped/screwed a scrap piece of wood under the plywood to produce much cleaner cuts.
I did paint the inside bottom white to make it easier to see the bottom and small pieces. I also drilled a pair of holes on each side to add rope handles.