  Central to the AdS/CFT correspondence is a precise relationship between the
curvature of an anti-de Sitter (AdS) spacetime and the central charge of the
dual conformal field theory (CFT) on its boundary. Our work shows that such a
relationship can also be established for tensor network models of AdS/CFT based
on regular bulk geometries, leading to an analytical form of the maximal
central charges exhibited by the boundary states. We identify a class of
tensors based on Majorana dimer states that saturate these bounds in the large
curvature limit, while also realizing perfect and block-perfect holographic
quantum error correcting codes. Furthermore, the renormalization group
description of the resulting model is shown to be analogous to the strong
disorder renormalization group, thus giving the first example of an exact
quantum error correcting code that gives rise to a well-understood critical
system. These systems exhibit a large range of fractional central charges,
tunable by the choice of bulk tiling. Our approach thus provides a precise
physical interpretation of tensor network models on regular hyperbolic
geometries and establishes quantitative connections to a wide range of existing
models.
