The gauge-theoretic Lagrangian lattice approaches are afflicted
by a number of technical difficulties. Reflection positivity can
be shown for some of the models, but generally requires the
inclusion of a factor sign
in the Lagrangian. Obtaining qualitative non-perturbative
information about the phase structure requires a non-trivial
measure input. The complicated functional form of the Lagrangian
and the metricity condition that has to be imposed via a Lagrange
multiplier and the corresponding functional integration do not
make conformal and higher-derivative theories attractive
candidates for numerical simulations. The compact version of
Smolin's de Sitter gravity is still the simplest model, but its
numerical investigation did not yield interesting results.