BISHOP, an american friend of mine has a very reliable 7.5" It is possible to get the AR15 reliable with short barrels but sometimes with a lot of tweaking. Buffer weights, return springs, feed ramps, gas port size, chamber dimensions, gas tube style, extractors, etc, etc. It becomes a great big balancing act sometimes. I think from experience that once you dip below 16" you start having reliability problems. 14.5" and you might see a jam every 100rds, 11.5 and down you start drinking to forget your rifle.
I let my friends have the real short AR's and I enjoy mt 16". Why? It was a discussion a few years back with my buddys that the barrels 14.5" and under were as reiable as my 16" and you know.... we had a test done. One 14.5" had 1 jam in the 100rds fired. The rifle was new and had only 100 rds through it before that. The other 14.5 had about 1 jam every 5th rd. He got mad and had a fit when I suggested a few things. He explained that it was dirty and was the only thing jaming the rifle. He said it had about 500rds through it without cleaning. hmmm. So there I began. I went with G17guy to the range 3 times over the next week and without cleaning shot 500rds. I had 1 jam.
You get less gas pressure operating the action with a short barrel. That pressure acts for a shorter time when you go below 14.5" thus you must start dicking around to get the right ballance with the above items. The 16" is a nice easy way to get the carbine to work. The longer barrel by 1.5" lengthens the durration that gasses act on the bolt carrier and make up for the lower gas pressure.
Parting words: I'm not new at this stuff. Bought my first of many AR15's in the 80's and have a bit of experience with these things, but what the hell, hey you 14.5" and under guys let the flames begin.
Moe