  We consider the problem of estimating $\mathbb{E} [f(U^1, \ldots, U^d)]$,
where $(U^1, \ldots, U^d)$ denotes a random vector with uniformly distributed
marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for
solving this kind of high-dimensional numerical integration problem. In the
case of dependent components of the random vector $(U^1, \ldots, U^d)$ one can
achieve more accurate results by using Latin hypercube sampling with dependence
(LHSD). We state a central limit theorem for the $d$-dimensional LHSD
estimator, by this means generalising a result of Packham and Schmidt.
Furthermore we give conditions on the function $f$ and the distribution of
$(U^1, \ldots, U^d)$ under which a reduction of variance can be achieved.
Finally we compare the effectiveness of Monte Carlo and LHSD estimators
numerically in exotic basket option pricing problems.
