  As recently pointed out in the field of Global Sensitivity Analysis (GSA) of
computer simulations, the use of replicated Latin Hypercube Designs (rLHDs) is
a cost-saving alternative to regular Monte Carlo sampling to estimate
first-order Sobol' indices. Indeed, two rLHDs are sufficient to compute the
whole set of those indices regardless of the number of input variables. This
relies on a permutation trick which, however, only works within the class of
estimators called Oracle 2. In the present paper, we show that rLHDs are still
beneficial to another class of estimators, called Oracle 1, which often
outperforms Oracle 2 for estimating small and moderate indices. Even though
unlike Oracle 2 the computation cost of Oracle 1 depends on the input
dimension, the permutation trick can be applied to construct an averaged
(triple) Oracle 1 estimator whose great accuracy is presented on a numerical
example.
  Thus, we promote an adaptive rLHDs-based Sobol' sensitivity analysis where
the first stage is to compute the whole set of first-order indices by Oracle 2.
If needed, the accuracy of small and moderate indices can then be reevaluated
by the averaged Oracle 1 estimators. This strategy, cost-saving and
guaranteeing the accuracy of estimates, is applied to a computer model from the
nuclear field.
