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.