  We construct the lattice AdS geometry. The lattice AdS$_2$ geometry and
AdS$_3$ geometry can be extended from the lattice AdS$_2$ induced metric, which
provided the lattice Schwarzian theory at the classical limit. Then we use the
lattice embedding coordinates to rewrite the lattice AdS$_2$ geometry and
AdS$_3$ geometry with the manifest isometry. The lattice AdS$_2$ geometry can
be obtained from the lattice AdS$_3$ geometry through the compactification
without the lattice artifact. The lattice embedding coordinates can also be
used in the higher dimensional AdS geometry. Because the lattice Schwarzian
theory does not suffer from the issue of the continuum limit, the lattice
AdS$_2$ geometry can be obtained from the higher dimensional AdS geometry
through the compactification, and the lattice AdS metric does not depend on the
angular coordinates, we expect that the continuum limit should exist in the
lattice Einstein gravity theory from this geometric lattice AdS geometry.
Finally, we apply this lattice construction to construct the holographic tensor
network without the issue of a continuum limit.
