  Aging in phase-ordering kinetics of the $d=3$ Ising model following a quench
from infinite to zero temperature is studied by means of Monte Carlo
simulations. In this model the two-time spin-spin autocorrelator $C_\text{ag}$
is expected to obey dynamical scaling and to follow asymptotically a power-law
decay with the autocorrelation exponent $\lambda$. Previous work indicated that
the lower Fisher-Huse bound of $\lambda\geq d/2 = 1.5$ is violated in this
model. Using much larger systems than previously studied, the instantaneous
exponent for $\lambda$ we obtain at late times does \emph{not} disagree with
this bound. By conducting systematic fits to the data of $C_\text{ag}$ using
different ansaetze for the leading correction term, we find $\lambda =
1.58(14)$ with most of error attributed to the systematic uncertainty regarding
the ansaetze. This result is in contrast to the recent report that below the
roughening transition universality might be violated.
