  A vertex $v$ in a porous exponential dominating set assigns weight
$\left(\tfrac{1}{2}\right)^{dist(v,u)}$ to vertex $u$. A porous exponential
dominating set of a graph $G$ is a subset of $V(G)$ such that every vertex in
$V(G)$ has been assigned a sum weight of at least 1. In this paper the porous
exponential dominating number, denoted by $\gamma_e^*(G)$, for the graph $G =
C_m \times C_n$ is discussed. Anderson et. al. proved that
$\frac{mn}{15.875}\le \gamma_e^*(C_m \times C_n) \le \frac{mn}{13}$ and
conjectured that $\frac{mn}{13}$ is also the asymptotic lower bound. We use a
linear programing approach to sharpen the lower bound to $\frac{mn}{13.7619 +
\epsilon(m,n)}$.
