  Constructing active sets is a key part of the Multivariate Decomposition
Method. An algorithm for constructing optimal or quasi-optimal active sets is
proposed in the paper. By numerical experiments, it is shown that the new
method can provide sets that are significantly smaller than the sets
constructed by the already existing method. The experiments also show that the
superposition dimension could surprisingly be very small, at most 3, when the
error demand is not smaller than $10^{-3}$ and the weights decay sufficiently
fast.
