This article is from the Star Trek Tech FAQ, by Joshua Bell inexorabletash@hotmail.com with numerous contributions by others.
Under ideal conditions, Warp 9.9997. (TNG TM, page 99) This is "sixty
times faster than the fastest starship, either existing or predicted"
- assuming traditional warp technology.
The Encyclopedia says that with boosters and relays, Warp 9.9999 is
the speed.
 
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