  We present a large-scale combinatorial-diagrammatic computation of high-order
contributions to the strong-coupling Kato-Takahashi perturbation series for the
Hubbard model in high dimensions. The ground-state energy of the
Mott-insulating phase is determined exactly up to the 15-th order in 1/U. The
perturbation expansion is extrapolated to infinite order and the critical
behavior is determined using the Domb-Sykes method. We compare the perturbative
results with two dynamical mean-field theory (DMFT) calculations using a
quantum Monte Carlo method and a density-matrix renormalization group method as
impurity solvers. The comparison demonstrates the excellent agreement and
accuracy of both extrapolated strong-coupling perturbation theory and quantum
Monte Carlo based DMFT, even close to the critical coupling where the Mott
insulator becomes unstable.
