Before revision:  In some parameter regimes, our algorithm is best known, and essentially confirms a conjecture of Ailon and Chazelle}  ] ] .
After revision:  In some parameter regimes, our algorithm is best known, and essentially confirms a conjecture of Ailon and Chazelle} ]. (3) We show that by fixing the angle in the Kac walk to be \pi/4 throughout, one obtains optimal JL and RIP transforms with almost the same running time, thereby confirming -- up to a \log\log{d ] .