  A recently developed lattice method for large numbers of strongly interacting
nonrelativistic fermions exhibits a heavy tail in the distributions of
correlators for large Euclidean time {\tau} and large number of fermions N,
which only allows the measurement of ground state energies for a limited number
of fermions using standard techniques. In such cases, it is suggested that
measuring the log of the correlator is more efficient, and a cumulant expansion
of this quantity can be exactly related to the correlation function. The
cumulant expansion technique allows us to determine the ground state energies
of up to 66 unpolarized unitary fermions on lattices as large as
72$\times$14^3, and up to 70 unpolarized unitary fermions trapped in a harmonic
potential on lattices as large as 72$\times$64^3. We have also improved our
lattice action with a Galilean invariant form for the four-fermion interaction,
which results in predictive volume scaling of the lowest energy of three
fermions in a periodic box and in good agreement of our results for N \leq 6
trapped unitary fermions with those from other benchmark calculations.
