  The quantum Hamming bound was originally put forward as an upper bound on the
parameters of nondegenerate quantum codes, but over the past few decades much
work has been done to show that many degenerate quantum codes must also obey
this bound. In this paper, we show that there is a Hamming-like bound stricter
than the quantum Hamming bound that applies to degenerate $t$-error-correcting
stabilizer codes of length greater than some positive integer $N(t)$. We show
that this bound holds for all single-error-correcting degenerate stabilizer
codes, forcing all but a handful of optimal distance-3 stabilizer codes to be
nondegenerate.
