For some time, Tom Rokicki has been working on lowing the upper bound for the face-turn metric of the Rubik’s cube. His main work (finished in Feb or March 2008) is described in http://tomas.rokicki.com/rubik25.pdf. More recently, John Welborn came up out of the blue and offered Tom CPU time on the “farm” of computers which Sony Imageworks uses to render animated movies. As a result of this generous offer, Tom was able to extend the same method used in the 25-move upper bound to show: in the face turn metric, every position can be solved in <=N moves, where N=20,21,22.
Based on the latest news (September 2014), we know every position can be solved in at most 20 moves in the face turn metric,, and at most 26 moves in the quarter turn metric.
Recently, New Scientist ran a short article on Tom’s result. Here is the link, though the full article requires a subscription: http://www.newscientist.com/channel/fundamentals/mg19926681.800-cracking-the-hardest-mystery-of-the-rubiks-cube.html .
An update is posted here: The Man Who Found God’s Number.