I have modified my coset solver to work in the quarter turn metric, and
with 396 cosets solved, I can announce that every cube position can be
solved in 32 or fewer quarter turns.

I am running phase one to a depth of 19 and letting phase two complete
the coset; each run takes about 12 minutes and approximately 63% of
the runs yield an upper bound of 25; the other 37% yield an upper
bound of 26.

No coset I have run yet has required more than 26 moves to solve, and
the possible distance-26 positions that I have run through an optimal
solver have all yielded distances less than 26, so I do not have a
new distance-26 position yet. (Applying Radu's symmetrical coset
idea to explore only symmetrical positions in the QTM would probably
provide a large collection of "hardest positions", much as it did
for the half turn metric.)

There are some improvements I can make to my existing technology for
the quarter turn metric, including some speed improvements to the
coset solver and leveraging local maxima information when combining
cosets into an overall bounds proof, and I will be exploring some of
these ideas.