The Oasis Moon Base is a biodome-like structure located on the side of the moon not facing Earth. It consists of offices and laboratories for T-Games staff, as well as a a closed ecological system to provide oxygen. It serves as a secondary base for T-Games - the primary base being the TBS Nightstar.
The Oasis Moon Base has not been revealed via any levels on LittleBigPlanet or in any creations in Minecraft, however it was originally planned to make an appearance at the end of Tremors. The idea was decided against as it was thought to make the story too complicated.