There is no legal prohibition actually on owning an M16 provided one meets the mostly financial requirements of the law which are open to all non-felons.
Current Federal law prohibits the sale of newly manufactured fully automatic weapons, so now we have a limited and aging supply of NFA guns. This is clearly contrary to the "well-regulated" provision of the 2nd Amendment. It is impossible to characterize a militia which is incapable of carrying out its mission as "well-regulate." The Constitutionally defined missions of the militia according to Article 1 Section 8 are to a) enforce the laws of the US b) suppress rebellions and c) defend against foreign invasion. If the militia was going to actually defend against foreign invasion full auto weapons would be required, and are now, no where near as widely available as is realistically needed to perform the mission.