  Extensive computations of ground state energies of the Edwards-Anderson spin
glass on bond-diluted, hypercubic lattices are conducted in dimensions
d=3,..,7. Results are presented for bond-densities exactly at the percolation
threshold, p=p_c, and deep within the glassy regime, p>p_c, where finding
ground-states becomes a hard combinatorial problem. Finite-size corrections of
the form 1/N^w are shown to be consistent throughout with the prediction
w=1-y/d, where y refers to the "stiffness" exponent that controls the formation
of domain wall excitations at low temperatures. At p=p_c, an extrapolation for
$d\to\infty$ appears to match our mean-field results for these corrections. In
the glassy phase, w does not approach the value of 2/3 for large d predicted
from simulations of the Sherrington-Kirkpatrick spin glass. However, the value
of w reached at the upper critical dimension does match certain mean-field spin
glass models on sparse random networks of regular degree called Bethe lattices.
