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I am still confused. If the barrel is shorter than 20" it is technically a carbine. But it depends on where your gas block or front sight, and gas tube length? Why would I need a mid length, why would I need more or less barrel in front of my front sight base.
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Carbine, as a word, means short rifle. Hence the "any AR-15 with a barrel less than 20" is a carbine"
Carbine is also a description of gas system length - because that was the length of the gas system on the first AR-15 carbines. One term is derived from the other, but they are not the same in practice.
For SHOPPING purposes, you must choose either a carbine, mid length or rifle gas system. Most these days seem to prefer the mid length, because it duplicates the dwell time of the rifle gas system in a shorter barrel. If you really want a 16" barrel, a mid length gas system is the mostly likely to give you trouble free operation.
The more or less barrel in front of the sight base, while an important technical feature, was my way of describing the systems to you, since you seem incapable or unwilling of doing any reading or research of your own.
So get a mid-length. Or don't. I don't care.