Starbase 4112 was a Federation starbase administered by Starfleet.
In 2369, the USS Quiele was refitted at this base. (TNG: "Aquiel", production art)
This starbase was only mentioned in writing.
This starbase has the highest number of the canonical starbases.
According to the Star Trek Encyclopedia (3rd ed., p. 466), after "The Neutral Zone" had aired, where Starbase 718 was mentioned in dialogue, it was decided that the starbase numbers shouldn't go much higher than 500.