Mine are all mediums now because that's what size frame I run, but when building a deep long Langstroth hive I have done this:
Make the frame rabbets 3/4" deep. This leaves 3/8" beespace at the top. Rip the boards for the sides 10 1/2" wide. Use 1/4" luan for the bottom The "ends" should be 19 7/8" I would make the sides 46 1/2". This means with the ends screwed on the total length will be 48". Cut the frame rabbets 3/8" wide and 3/4" deep. You can do this with two cuts on the table saw or you can use a dado blade and do it with one cut. I make a butt joint with the ends running past, but if you want to make finger joints they will hold better. Screw together with 2" deck screws. The bottom is 19 7/8" by 48". Nail, staple or screw it on. I would make the top out of 3/4" plywood, 20" by 48". I like a small top entrance on the end, so I would chisel or route an entrance into the cover so they have 1/4" to 3/8" tall 2" long entrance. It is nice, but not necessary, to have some kind of smaller inner covers so you don't have to expose all the bees at once. Say 6" x 20" strips of 1/4" luan plywood and put those on before the cover. I would set all of this on bricks, blocks or treated wood. If I put legs on them they blow over...