  We discuss the optimal detection strategy for a stochastic background of
gravitational waves in the case n detectors are available. In literature so
far, only two cases have been considered: 2- and n-point correlators. We
generalize these analysises to m-point correlators (with m<n) built out of the
n detector signals, obtaining the result that the optimal choice is to combine
2-point correlators. Correlating n detectors in this optimal way will improve
the (suitably defined) signal-to-noise ratio with respect to the n=2 case by a
factor equal to the fourth root of n(n-1)/2. Finally we give an estimation of
how this could improve the sensitivity for a network of multi-mode spherical
antennas.
