We introduce a class of functions in d ≥ 3 dimensions which have arbitrary odd superposition effective dimensions between three and d inclusive. We prove that for the integration of any function in this class any Sobol’ points of a fixed length have zero error, whereas Owen’s scrambling of any Sobol’ points of the same length has the same variance of error as simple Monte Carlo meth- ods. Furthermore, for any function in the same class Owen’s scrambling of high- discrepancy points, which consist of d copies of the van der Corput points in base two, gives zero-variance estimates for the integration.