  We revisit the well-known Gilbert-Varshamov (GV) bound for constrained
systems. In 1991, Kolesnik and Krachkovsky showed that GV bound can be
determined via the solution of some optimization problem. Later, Marcus and
Roth (1992) modified the optimization problem and improved the GV bound in many
instances. In this work, we provide explicit numerical procedures to solve
these two optimization problems and hence, compute the bounds. We then show the
procedures can be further simplified when we plot the respective curves. In the
case where the graph presentation comprise a single state, we provide explicit
formulas for both bounds.
