Using a traditional box spring with a memory foam mattress defeats the reason you've chosen memory foam. Memory foam shapes itself to your body's weight, providing full sleep support. When your body presses on a memory foam mattress on top of a box spring, however, the foam's underside contours to the spring and pushes back. The end result is that you sink down into foam that responds with upward pressure, interfering with your circulation. The best foundation for a memory foam mattress is a flat platform, or none at all.