The theoretical velocity of a railgun-launched heavy shell

How fast could a 16-inch-class shell theoretically be fired with the best available or conceivable technology?

A working railgun could reach several times the speed of sound, but the exact velocity depends on the launcher and projectile.

The question is initially interpreted as projectile velocity rather than firing cycle. A functioning railgun paired with hypersonic projectile design could drive a nominal 16-inch-class shell to several times the speed of sound. The precise figure would depend on how well the electromagnetic launcher and projectile worked together. This identifies an order-of-magnitude opportunity rather than claiming a service-ready performance number. A later clarification addresses rate of fire as a separate mechanical problem.