Your description fits a German service rifle, originally an M1888 "Commission" model chambered for the M1888 RN .318" diameter bullet.
Some were re-barreled to use the M1905 spitzer (pointed) .323" diameter bullet, and were so marked on the receiver (1940). That .311" you measured was probably the bore diameter of the re-barreled piece (nominally .312" bore diameter).
SUHL is the city where arsenal was located, SCHILLING was the manufacturer in 1890. Barrel length would define if you indeed have the carbine version of the M1888. The sling fittings were same on both rifle and carbine versions. The open magazine bottom is for the Mannlicher-style ammo clip to fall through when the last round is chambered.
These old rifles are considered to marginally suitable for modern full-power 7.92x57 ammunition.