  We show the presence of Floquet-Weyl and Floquet-topological-insulator phases
in a stacked two-dimensional ring-network lattice. The Weyl points in the
three-dimensional Brillouin zone and Fermi-arc surface states are clearly
demonstrated in the quasienergy spectrum of the system in the Weyl phase. In
addition, chiral surface states coexist in this phase. The
Floquet-topological-insulator phase is characterized by the winding number of
two in the reflection matrices of the semi-infinite system and resulting two
gapless surface states in the quasienergy g ap of the bulk. The phase diagram
of the system is derived in the two-parameter space of hopping S-matrices among
the rings. We also discuss a possible optical realization of the system
together with the introduction of synthetic gauge fields.
