Vortex configurations in SO(3) \times Z(2)
  We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. Furthermore, there is an additional constraint coming from the boundary conditions. We propose an update algorithm that satisfies the constraints and is straightforward to implement. 
A. Alexandru, R. W. Haymaker