  A finite metric space is called here distance degree regular if its distance
degree sequence is the same for every vertex. A notion of designs in such
spaces is introduced that generalizes that of designs in $Q$-polynomial
distance-regular graphs. An approximation of their cumulative distribution
function, based on the notion of Christoffel function in approximation theory
is given. As an application we derive limit laws on the weight distributions of
binary orthogonal arrays of strength going to infinity. An analogous result for
combinatorial designs of strength going to infinity is given.
