While carbine gas has been around for awhile, I don't know of an issue rifle with 16" barrel that uses it.
The 14.5 inch barrel was specified by the military to facilitate the attachment of the issue bayonet. The selection of that barrel length had nothing to do with the gas system.
Colt introduced the AR15 SP1 Carbine (Model R6001) in September of 1977. Colt has cataloged the following 5.56 mm models with barrel lengths less then 20 inches and they ALL use a carbine length gas system.
R0605A M16A1 Carbine 14.5" barrel
R0605B M16A1 Carbine 14.5" barrel
R0607 SMG Tanker Model 10" barrel
R0607A SMG Tanker Model 10" barrel
R0607B SMG Tanker Model 10" barrel
R0608 Survival Rifle 10" barrel
R0609 XM177E1 Commando (US Army) 11.5" barrel
RO610 GAU-5/A USAF 10' barrel
R0610B SMG 10" barrel
R0619 XM177E1 Export Carbine 11.5" barrel
R0620 XM177 Export Carbine 10" barrel
R0629 XM177E2 SMG US Army 11.5" barrel
R0639 XM177E2 Export Model 11.5" barrel
R0640 M16 SMG 11.5" barrel
R0649 GAU-5/A/A USAF 10" barrel
R0651 M16A1 Carbine 14.5" barrel
R0652 M16 Carbine 14.5" barrel
R0720 M16A2 XM4 Carbine 14.5" barrel
R0721 M16A2 XM4A1 Carbine 14.5" barrel
R0723 M16A2 Carbine 14.5" barrel
R0723S M16A2 Carbine 14.5" barrel
R0723X M16A2 Carbine 14.5" barrel
R0725 M16A2 Carbine - UAE 15.5" barrel
R0725H M16A2 Carbine - Holland 15.5" barrel
R0727 M16A2 Carbine UAE 14.5" HBAR barrel
R0727 M16A2 Carbine UAE 14.5" barrel
R0728 M16A2 Carbine 14.5" M4 HBAR barrel
R0729 M16A2 Carbine 14.5" M4 HBAR barrel
R0733 M16A2 Commando 11.5" A1 barrel
R0734A M16A2 Commando 11.5" A1 barrel
R0734 M16A2 Commando 11.5" A1 barrel
R0735 M16A2 Commando 11.5" A1 barrel
R0735B M16A2 Commando - Brazil 11.5 A1 barrel
R0737 M16A2 Commando 11.5" A1 barrel
R0738 Enhanced Carbine 11.5" A1 barrel
R0770 M16A3 Carbine 14.5" HBAR barrel
R0777 M4 Carbine w/extended feed ramps and heavy buffer 14.5" M4 barrel
R0778 M4 Carbine w/extended feed ramps and heavy buffer 14.5" M4 barrel
R0779 M4 Carbine w/extended feed ramps and heavy buffer 14.5" M4 barrel
R0780 M16A3 Commando 11.5" A1 barrel
R0920 M4 14.5" M4 barrel
R0920AF M4 Carbine USAF 14.5" M4 barrel
R0921 M4A1 Carbine 14.5" M4 barrel
R0921HB M4A1 Carbine 14.5" M4 heavy carbine barrel
R09211 M4A1 Carbine - Israel 14.5" M4 barrel
R0925 M4A1 14.5" M4 barrel
R0927 M16A4 Carbine 14.5" M4 heavy carbine barrel
R0933 M16A4 Commando 11.5" A1 barrel
R0933CQB M4 Commando 11.5" A1 barrel
R0935G M16A4 Commando 11.5" A1 barrel
R0935 M16A4 Commando 11.5" A1 barrel
R0938 M4/M16A4 Commando HBAR 11.5" HBAR
R0977 M4 Carbine 14.5" M4 barrel
R0977CQB M4 Carbine 14.5" M4 barrel
R0978 M4 Carbine 14.5" M4 barrel
R0979 M4 Carbine 14.5" M4 barrel
R0979 M4 NYPD Carbine 14.5" M4 barrel
XM4 Carbine 14.5" A1 barrel
C8 Carbine Canada 14.5" A1 barrel
AR6320 Police Patrol Carbine 16" A1 barrel
AR6520 AR15A2 Government Carbine 16" A1 barrel
AR6520M AR15A2 Government Carbine Mexico 16" A1 barrel
AR6522 AR15A2 Government Carbine 16" A1 barrel
AR6525 AR15A2 Government HBAR Carbine 16.1" HBAR
AR6526 AR15A2 Government HBAR Carbine 16.1" HBAR
AR6530 Law Enforcement Light Weight Carbine 16" A1 barrel
AR6530M Law Enforcement Lightweight Carbine - Mexico 16" A1 barrel
AR6535 Law Enforcement Lightweight Carbine 16" A1 barrel
AR6536 California Highway Patrol Carbine 16" HBAR
AR6721 AR15A3 Tactical Carbine 16" HBAR
AR6731 Competition HBAR II Carbine 16.1" HBAR
LE6920 Law Enforcement Carbine 16.1" M4 barrel
LE6921 Law Enforcement HBAR Carbine 16.1" M4 heavy barrel
LE6921 Law Enforcement Carbine 14.5" M4 barrel
LE6922 Law Enforcement Carbine 16.1" M4 barrel
R6001 AR15 Sp-1 Carbine 16" Standard barrel
R6420 AR15A2 Sporter Carbine 16" A1 barrel
R6425 AR15A2 Sporter Carbine 16"A1 barrel
R6530 AR15A2 Government Carbine 16" A1 barrel
R6530 Sporter Lightweight 16" A1 barrel
R6721 AR15A3 Tactical Carbine 16" HBAR
MT6400C Match Target M4 Carbine 16" M4 barrel
MT6530 Match Target Light Weight 16" A1 barrel
MT6731 Match Target Competition HBAR II 16" HBAR
MT6731C Match Target Competition HBAR II 16" HBAR
MT6731HC Match Target Competition HBAR II 16" HBAR
As you can see Colt has produced millions of weapons in barrel lengths ranging from 10" to 16.1" over the years. Never have they built one with a mid length gas system. They all functioned as designed with a carbine gas system.
Mid length gas systems were developed to correct problems people were having building their M4gerys from out of spec aftermarket parts. They are NOT necessary for a properly functioning weapon if you use the correct parts building your carbine. That means you have to pony up and pay for barrels with the gas port cut to the correct diameter and use the correct buffer spring, buffer and disconnector.
I reject the idea that mid length gas systems are somehow better. Colt, who owned the AR/M16 pattern world never felt the need for them.