(I have also tried emailing the authors. Well, I emailed one of them,
who didn't reply, and although I've emailed the others I'm a bit wary
of waiting too long for a reply, so...)

If anyone else on here has read "Multidimensional Extension of
Matsui's Algorithm 2", I'm having serious trouble with part of it.

Equation (18) is obtained by solving Equation (9) (using the by-then
obtained means and variances for distributions a and R). However, I've
plugged the values for mean and variance into Equation 9, and:

* There seems to be no way to rearrange it to obtain an equation in
terms of N.

* There seems to be no way to obtain a formula containing the term
Phi^{-1}(2*P_S - 1) from it. I can see how, at the start of the
rearrangement, the term Phi^{-1}(P_S) appears on one side, but as Phi
is not affine, this is as far as I can go.

* The wording appears to indicate that the variance sigma_a^2 is
negligible and should be approximated by zero. If anyone's managed to
obtain the equation for N independently, can they confirm or deny
this?

Many thanks,

James McLaughlin.