Artillery Assignment

[scorpio_rocks]

From the Game Guide:

What is the minimum range for indirect artillery fire?

Artillery have a built-in minimum range, 20% of their max range and locked to a maximum of 20 hexes, minimum of 5. So only some very short range on-map infantry guns will tend to have a min range of 5-19 hexes in reality. (There has never been any distinction between guns, rockets, or howitzers as to min range in the game series).
It's not spelled out in any detail in any manuals since it is obvious from the fact that the "cannot fire" indicator is shown if you try to plot the gun on too close a target hex in the bombardment screen. Mousing over the red circle gives an explanatory message.
If you really need to fire indirect at close-in enemy targets - then issue mortars to your troops, not infantry guns.