In 2364, the location of Starbase 4077 was labeled on the map Starbase Ops Status Sol Sector. (TNG: "Conspiracy", display graphic)
The location of this base was depicted twice on the star chart. Starbase 4077 is the highest numbered starbase in the series. According to the Star Trek Encyclopedia (3rd ed., pg. 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.