Asymptotic improvement of GV bound

The Gilbert-Varshamov (GV) bound is a well-known lower bound in coding theory that claims that for any given code with relative distance $\delta$, there is a lower bound for the rates possible. This paper will asymptotically improve upon by 1.5$\frac{\log n}{n}$ for unconstrained binary systems. We also show that for the RLL(0,1) constrained system, we can achieve rates $2\log \phi - \log \tau$, where $\tau$ is the asymptotic of the total ball size for the RLL(0,1) constrained systemBachelor of Science in Mathematical Science