  There are a number of situations where, when computing prices of financial
derivatives using quasi-Monte Carlo (QMC), it turns out to be beneficial to
apply an orthogonal transform to the standard normal input variables. Sometimes
those transforms can be computed in time $O(n\log(n))$ for problems depending
on $n$ input variables. Among those are classical methods like the Brownian
bridge construction and principal component analysis (PCA) construction for
Brownian paths.
  Building on preliminary work by Imai and Tan [3] as well as Wang and Sloan
[13], where the authors try to find optimal orthogonal transform for given
problems, we present how those transforms can be approximated by others that
are fast to compute.
  We further present a new regression-based method for finding a Householder
reflection which turns out to be very efficient for a wide range of problems.
We apply these methods to several very high-dimensional examples from finance.
