Starbase 718 was a Federation starbase administered by Starfleet.

In 2364, Captain Jean-Luc Picard was summoned to an emergency conference at this starbase. (TNG: "The Neutral Zone")

This starbase was only mentioned in dialogue.
According to the Star Trek Encyclopedia (4th ed., vol. 2, p. 318), after "The Neutral Zone" had aired, it was decided that the starbase numbers shouldn't go much higher than 500.
According to Star Trek: Star Charts (p. 66, "United Federation of Planets I") and Stellar Cartography: The Starfleet Reference Library ("Federation Historical Highlights, 2161-2385"), Starbase 718 was located in the Beta Quadrant.

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