Sequentially refined Latin hypercube designs: reusing every point

This approach conducts an initial experiment with a computer code using a Latin hypercube design and then runs a follow-up experiment with additional runs elaborately chosen so that the combined design set for the two experiments forms a larger Latin hypercube design. This augmenting process can be repeated multiple stages, where in each stage the augmented design set is guaranteed to be a Latin hypercube design.

We provide a theoretical framework to put this approach on a firm footing. Numerical examples are given to corroborate the derived theoretical results.