  We study the effective spin-orbital model that describes the magnetism of
4$d^1$ or 5$d^1$ Mott insulators in ideal tricoordinated lattices. In the limit
of vanishing Hund's coupling, the model has an emergent SU(4) symmetry which is
made explicit by means of a Klein transformation on pseudospin degrees of
freedom. Taking the hyperhoneycomb lattice as an example, we employ parton
constructions with fermionic representations of the pseudospin operators to
investigate possible quantum spin-orbital liquid states. We then use
variational Monte Carlo (VMC) methods to compute the energies of the projected
wave functions. Our numerical results show that the lowest-energy quantum
liquid corresponds to a zero-flux state with a Fermi surface of four-color
fermionic partons. In spite of the Fermi surface, we demonstrate that this
state is stable against tetramerization. A combination of linear flavor wave
theory and VMC applied to the complete microscopic model also shows that this
liquid state is stable against the formation of collinear long-range order.
