Model 1916 Carbines
The Model 1916 carbine is simply a Model 1916 action with a carbine-length barrel.  Like many of the 1916's, it has no markings to indicate where it was made, although they presumably manufactured at Oviedo.. Other variations that have been observed are not stocked all the way to the end of the barrel.
Collectible Firearms Photo used with Permission
Collectible Firearms Photo used with Permission
A top view of the action is shown below.  Note the lack of markings, the thumb cut in the left side of the receiver wall, and the carbine sight.
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Serial Numbers and Production

So far, I have only seen plain serial numbers (no letter prefix) with the top one being 89XX.  Based on these observations, the total production is estimated to be about 10,000.
The picture shown below is actually a Paraguayan 1893 Carbine, but shows what a Spanish 1916 carbine that is not stocked to the muzzle looks like.
Collectible Firearms photo, used with permission
Page Updated
on 10/06/09
Serial Numbers
1916C1
1916C2
1916C3