  We identify recurrent ingredients in the antithetic sampling literature
leading to a unified sampling framework. We introduce a new class of antithetic
schemes that includes the most used antithetic proposals. This perspective
enables the derivation of new properties of the sampling schemes: i) optimality
in the Kullback-Leibler sense; ii) closed-form multivariate Kendall's $\tau$
and Spearman's $\rho$; iii)ranking in concordance order and iv) a central limit
theorem that characterizes stochastic behavior of Monte Carlo estimators when
the sample size tends to infinity. Finally, we provide applications to Monte
Carlo integration and Markov Chain Monte Carlo Bayesian estimation.
