I'll be curious about the answers to this as well. I've read that a 4 foot by 2 foot is sufficient for up to 12 quail. I currently have a 4x2 with 8 quail and so far no issues (6 female/2 male). But I'm thinking about maybe breaking that up a bit with a divider down the middle and 3/1 on each side.
But I'm a newbie so I'll look forward to more experienced input :)
IMO you are going at it the wrong way. I'd start from "how much room can I give them, while keeping costs, required space and other concerns (like the weight/mobility of the cage, ease of egg collection and similar) at a reasonable level?".
That said, I think the usual recommendation for coturnix is 1 square foot per bird. But I believe I've heard of even less than ½ square foot per bird.
Build your cage no more than 2' deep unless you've got really long arms. If you want sloping floors so the eggs roll to the front, make the rear 9" and the front 11". If you make the floor flat, then make it 10 - 11" or else they'll be bonking their heads and you'll have injured or dead quail. Make the length 2, 3, or 4' long. What ever works for your space. My cages for my breeders are almost 4' long. I keep 1 male and 5-6 females to a cage. There is a sand box and a hiddy hole space for them to separate themselves if the need to. I use an oil drip pan that's 26" x 47" that I buy at Walmart as a dropping pan under the cages. Use 1/2" x 1" wire mesh for the floor. If you make sloping floors, then place the wire so the 1 inch slot runs front to back and the wires are on top so the eggs will roll. Walls can be 1?2" x 1/2" or 1" x 1" though they will stick their heads thru the 1x1 sometimes. Ceilings can be anything up to 1" x 1"
I highly recommend that you make the cage totally out of wire and hang it from a wooden structure. Cleaning poo off of wood is just not worth it.