Floor 16 was a location aboard the city-sized JMC mining spaceship Red Dwarf. Floor 16 was 2,567 floors below the Z Shift sleeping quarters, and contained amenities such as a showering room for the crew.
Most notably, Floor 16 was the location of a faulty stasis booth which preserved the area around it due to a stasis leak. Three million later, this would provide the boys from the Dwarf with a way of traveling back in time to before the accident which killed the rest of the crew.
Following instructions from Rimmer's old diary, the gang took an Xpress Lift with it's own hostess down to Floor 16. Here they find a hidden stasis leak where the past has leaked into the room, and which acts as a doorway to the past, to a little while before the crew all died. They go through and come out the other side, embarrassingly right into a shower room where they bump in to a man in the shower.
Lister then went off to find his old girlfriend Kochanski, first finding his old friend Olaf Petersen. Lister's search would eventually lead him off-ship to the Ganymede Holiday Inn. Rimmer went off to unsuccessfully warn his past self, who was tripping out on Titan Mushrooms at the time. ("Stasis Leak", Series II)