  The Coulomb branch of 3-dimensional N=4 gauge theories is the space of bare
and dressed BPS monopole operators. We utilise the conformal dimension to
define a fan which, upon intersection with the weight lattice of a GNO-dual
group, gives rise to a collection of semi-groups. It turns out that the unique
Hilbert bases of these semi-groups are a sufficient, finite set of monopole
operators which generate the entire chiral ring. Moreover, the knowledge of the
properties of the minimal generators is enough to compute the Hilbert series
explicitly. The techniques of this paper allow an efficient evaluation of the
Hilbert series for general rank gauge groups. As an application, we provide
various examples for all rank two gauge groups to demonstrate the novel
interpretation.
