Not quite, Germany was limited in the number of guns in military calibers, mostly 8x57, it could have under the Versailles treaty. Hunting weapons could be produced as long as they were not in military calibers, leading for example to many 8x57 guns rechambered in 8x60, and the popularity of the 7x64 round.
For the OP, there should be a set of proof marks under the barrel if you take it out of the stock. That will probably give you the date of manufacture.
F 135 - the right choice