All depends on how many you want to raise. Build with as large of floor plan as you see reasonable. Those GIANTS don't fly much.If/when I build an aviary for giant runt pigeons how big would it need to be? I've only seen giant runt pigeons in person once.
An option is to build a loft, (what ever size you choose) and a tractor style aviary attached or movable. Not much height needed.