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Constructing active sets is a key part of the Multivariate DecompositionMethod. An algorithm for constructing optimal or quasi-optimal active sets isproposed in the paper. By numerical experiments, it is shown that the newmethod can provide sets that are significantly smaller than the setsconstructed by the already existing method. The experiments also show that thesuperposition dimension could surprisingly be very small, at most 3, when theerror demand is not smaller than $10^{-3}$ and the weights decay sufficientlyfast.

Small Superposition Dimension and Active Set Construction for Multivariate Integration Under Modest Error Demand