Simulation of correlated normal random variables

Simulation of i.i.d. normal random variables is standard. Let us consider the Cholesky decomposition

$$\Sigma = CC^t$$ (47)

of the covariance matrix $\Sigma$. If $Z=(Z_i)_{i=1,\ldots,d+2}$ are $d+2$ i.i.d. normal random variables, then

$$(N_i)_{i=1,\ldots,d+2} = N = C\cdot Z$$ (48)

contains $d+2$ normally distributed random variables with covariances $\Sigma$.