The Great Experiment was a nickname that was used to describe the first extrasolar colonization of the planet Terra Nova during the 21st century. (ENT: "Terra Nova")
By the 23rd century, the nickname was applied to the USS Excelsior, the prototype of the successful Excelsior-class. She was noted as such for having been outfitted with transwarp drive. (Star Trek III: The Search for Spock)