Starbase 718 was a Federation starbase administered by Starfleet. This base was located near the Romulan Neutral Zone. In 2364, Captain Jean-Luc Picard attended a conference there. (TNG: "The Neutral Zone")
According to the Star Trek Encyclopedia (3rd ed., pg. 466), after "The Neutral Zone" had aired, it was decided that the starbase numbers shouldn't go much higher than 500.