Hypothetically, the maximum velocity attainable by any projectile would be the same velocity of the gases from the expanding propellant as they leave the barrel. However, to achieve that feat, it would require laboratory conditions and systems set up to ensure the projectile can be accelerated up to such velocities. A typical 16" barrel does not offer the space necessary for such an acceleration.
Back in the 80's, NASA developed a theoretical method for interstellar space travel called the "Orion Project". The idea was to have a spacecraft that was built with a "magazine" loaded with dozens of small nuclear warheads. At the rear of the spacecraft was a massive metal 'pusher plate', designed to capture and absorb the force of the atomic blasts, transferring them into the overall momentum of the ship. As the spacecraft set sail, the bombs would be launched at timed intervals from the pod, whereupon they would detonate at a predetermined distance behind the ship. With each explosion, the ship would gain velocity. At a certain point, the ship would be accelerated to the same velocity as that of the matter expanding from the blast waves, making it the fastest manned vessel ever launched in human history. The Orion starship was calculated to be able to reach the Alpha Centauri system in just under 200 years, with the crew spending most of their time aboard in cryogenic hibernation.
Very interesting concept indeed, but there is this one question: How would you decelerate the ship now once it reaches it's destination? The only feasible solution would be to turn the entire vessel around via attitude-control jets, and explode a series of warheads, this time in the front of the ship. Which is going to force it, and it's crew to fly through a white-hot and extremely radioactive plasma smog of it's own exhaust. Not to mention the fact that the ship would also be forced to carry at least 100 times more mass than it was intended to be, due to the inverse square law of increasing mass versus the amount of fuel that would be needed to accelerate/decelerate at the same rate of speed. So, within a few years, research on this project was scrapped.
Now back to the subject of the maximum velocity of a projectile attainable under terrestrial conditions: Remember the news articles in the past about how suicidal individuals jumped off from very tall bridges and the subsequent autopsies on these individuals revealed that they actually died from the blunt force impact of STRIKING the water's surface and not by drowning? Air is not as dense as water but works the same way. When something travels fast enough, air would become so compressed ahead of it that it will act on the object as a solid state of matter. If a bullet can be accelerated to such a speed, it's interaction with this super-compressed mass of air ahead of it would destroy it. If it survives this force and manages to keep on plowing ahead, it will lose it's momentum very rapidly through the generation of heat, much akin to a spacecraft "burning up" as it reenters the Earth's atmosphere.
Target and varmint shooters who experiment with super-hot reloads in small caliber rifles often report that some of their bullets would "blow up" or fragment in midflight before reaching the target. Those are usually in the 3500-4100 feet/sec range. I do not know of any small arms cartridge that ever exceeded the low 4000 feet/sec range. Even with the hottest wildcat loadings. In H. Beam Piper's "Paratime" series of novels, one of the 2nd Level civilizations called the 'Akor-Neb', which has a penchant for dueling and settling disputes by assassinations, built pistols that "fired 10-grain plastic bullets at 10,000 feet/sec", and reportedly had no issues with overpenetration because the round immediately disintegrated upon impact, transferring all of it's energy into the target's body. In real life, such a bullet would have disintegrated as soon as it began moving forward in the barrel of the gun, when it meets that solidly compressed tube of air ahead of it. It might not even survive the detonation of that type of powder that would cause it to achieve such velocity. And I highly doubt any material on Earth can be built into a pistol that would withstand the pressures from the use of such a propellant, which would be akin to the detonation of a plastic explosive.
It would be a really interesting experiment if someone were to neck down a .50 BMG to accept a super-streamlined .17 or .22 caliber match bullet, and fire it from a standard-length rifle barrel just to see how it will perform. From a remote-controlled rig of course.
And folks on Earth will have a new companion star to the Sun, shining just as bright as the Sun, for the next couple of days before it begins to dim and fade slowly.