  We propose a novel storage scheme for three-nucleon (3N) interaction matrix
elements relevant for the normal-ordered two-body approximation used
extensively in ab initio calculations of atomic nuclei. This scheme reduces the
required memory by approximately two orders of magnitude, which allows the
generation of 3N interaction matrix elements with the standard truncation of
$E_{\rm 3max}=28$, well beyond the previous limit of 18. We demonstrate that
this is sufficient to obtain the ground-state energy of $^{132}$Sn converged to
within a few MeV with respect to the $E_{\rm 3max}$ truncation.In addition, we
study the asymptotic convergence behavior and perform extrapolations to the
un-truncated limit. Finally, we investigate the impact of truncations made when
evolving free-space 3N interactions with the similarity renormalization group.
We find that the contribution of blocks with angular momentum $J_{\rm rel}>9/2$
to the ground-state energy is dominated by a basis-truncation artifact which
vanishes in the large-space limit, so these computationally expensive
components can be neglected. For the two sets of nuclear interactions employed
in this work, the resulting binding energy of $^{132}$Sn agrees with the
experimental value within theoretical uncertainties. This work enables
converged ab initio calculations of heavy nuclei.
