Hyper-subspace

Hyper-subspace was a measure of speed that surpassed the standard Federation warp factor.

Technology utilizing hyper-subspace speeds was first conceived of in the late 24th century by the Pathfinder Project, seeking to find a way to contact the Federation starship USS Voyager in 2376, lost in the Delta Quadrant since the beginning of the decade. They managed to establish a momentary communication link by using the MIDAS array to create an artificial wormhole from the Alpha Quadrant to the Delta Quadrant, then sending a transmission through which Voyager detected and received. Voyager was sent the specifications for the hyper-subspace technology and immediately set out to equip their communications array with it. 

Later that year, the project's work established a more permanent link between the MIDAS array and Voyager, via a cyclic pulsar with a peak every thirty-two days, allowing contact once a month. Voyager, which could then transmit hyper-subspace messages independently, would be sent a data stream containing updates on the Alpha Quadrant, and more importantly, letters from home. Upon receiving the data stream, Voyager had approximately seventeen hours to compile and send their response before the pulsar fell out of alignment. 

In the months before their return to the Alpha Quadrant, the crew made yet another breakthrough. Operation Watson was a method for a establishing a real-time link between Starfleet Command and Voyager. The project involved bouncing a phased tachyon beam, containing a triaxilating signal, off a quantum singularity. The singularity only stayed in alignment for eleven minutes per day, allowing only this brief time each day for communication.