The location of Starbase 0834
Starbase 0834 was a Federation starbase administered by Starfleet. This base was located in Sector 001, which was a region of space in the Alpha Quadrant. It was located near the Sol system, Orion Sector Tactical Command, Starbase 74, and Starbase 4077. (TNG: "Conspiracy", display graphic)
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.