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In this paper we use counting arguments to prove that the expected percentagecoverage of a $d$ dimensional parameter space of size $n$ when performing $k$trials with either Latin Hypercube sampling or Orthogonal sampling (when$n=p^d$) is the same. We then extend these results to an experimental designsetting by projecting onto a 2 dimensional subspace. In this case the coverageis equivalent to the Orthogonal sampling setting when the dimension of theparameter space is two. These results are confirmed by simulations. The ideaspresented here have particular relevance when attempting to perform uncertaintyquantification or when building populations of models.

Estimates of the coverage of parameter space by Latin Hypercube and  Orthogonal sampling: connections between Populations of Models and  Experimental Designs