There could be two companies that made that knife. The first one is Smokey Mountain Knife Works and almost all of their REMINGTON Knives ware made by Camillus Cutlery Company. The second one is Carolina Knife Works which was owned by Blackie Collins, (Deceased) he also owned Bowen Knife Company and they made a lot of Bullet Knives and other Remington knives. They were famous for using Wessonwood on their knife handles. You may want to talk with Kevin Pipes at SMKW and see if he can provide any more guidance.

When Remington moved their knife making to Madison, North Carolina, the Logo they imprinted had a bullet through it.  This knife does not have that, so it probably was not made there, but is probably not a much older knife.

The one Remington reference I have does not list an R 16 model, and I can't find anything online that lists it either.  Sorry I can't be of more help, but since you have this knife, enjoy it.

This caused me to spend some time looking for it, which was totally wasted since I couldn't find anything to help you.  I have two remington references and neither has anything on the particular model.  Sorry I can't help.