Code for MVN CDFs
Take a look at http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/mvncdf.htm and its links to Genz's work.
Permutation probabilities
Pruning permuation trees
Take a look at http://www.itl.nist.gov/div898/software/dataplot/refman2/auxillar/mvncdf.htm and its links to Genz's work.