  We evaluate the ground state degeneracy of noncommutative Chern-Simons models
on the two-torus, a quantity that is interpreted as the "topological order" of
associated phases of Hall fluids. We define the noncommutative theory via
T-duality from an ordinary Chern-Simons model with non-abelian 't Hooft
magnetic fluxes. Motivated by this T-duality, we propose a discrete family of
noncommutative, non-abelian fluid models, arising as a natural generalization
of the standard noncommutative Chern-Simons effective models. We compute the
topological order for these universality classes, and comment on their possible
microscopic interpretation.
