  We present a numerical study of ground states of the dilute versions of the
Sherrington-Kirkpatrick (SK) mean-field spin glass. In contrast to so-called
"sparse" mean-field spin glasses that have been studied widely on random
networks of finite (average or regular) degree, the networks studied here are
randomly bond-diluted to an overall density $p$, such that the average degree
diverges as $\sim pN$ with the system size $N$. Ground-state energies are
obtained with high accuracy for random instances over a wide range of fixed
$p$. Since this is a NP-hard combinatorial problem, we employ the Extremal
Optimization heuristic to that end. We find that the exponent describing the
finite-size corrections, $\omega$, varies continuously with $p$, a somewhat
surprising result, as one would not expect that gradual bond-dilution would
change the $T=0$ universality class of a statistical model. For $p\to1$, the
familiar result of $\omega(p=1)\approx\frac{2}{3}$ for SK is obtained.
