Engineering at its Peak
Solid propellant guns launching full bore (no sabot) projectiles under practical conditions reach velocities in the 1300 to 1400 m/s range. Yes, you can go faster with sabot use, large charge masses, high pressures, and high temperatures but launch masses get smaller, projectile accelerations larger, and gun stress and wear higher. This is primarily related to the sound speed of the propellant combustion gases which directly effects how much of the pressure produced can push on the projectile as it moves down bore.
In laboratories, two stage light gas guns use helium or hydrogen as the projectile driver gas to reach higher velocities. A typical two stage light gas gun appears in the figure below. Due to their size and complexity they are difficult to weaponize.
Hydrogen combustion guns add oxygen to the hydrogen to create a lighter propellant which is capable of launching full bore projectiles to velocities in the 2500 to 3000 m/s range. The system is compact and can be weaponized.
Click picture to see gun firing