  We introduce the concept of multidimensional antithetic as the absolute
minimum of the covariance defined on the orthogonal group by $A\mapsto
Cov(f(\xi),f(A\xi))$ where $\xi$ is a standard $N$-dimensional normal random
variable and $f:\mathbb{R}^{N}\to\mathbb{R}$ is an almost everywhere
differentiable function. The antithetic matrix is designed to optimise the
calculation of $E[f(\xi)]$ in a Monte Carlo simulation. We present an iterative
annealing algorithm that dynamically incorporates the estimation of the
antithetic matrix within the Monte Carlo calculation.
