Let m be a positive integer, and let $\mathbb{T}$ denote the set of all subsets of $\{1,\ 2,\ \cdots,\ m\}$. Call a subset $\mathbb{S}$ of $\mathbb{T}$ ${\delta}-good$ if for all $s_1,\ s_2\in\mathbb{S}$, $s_1\ne s_2$, $\mid\Delta(s_1,\ s_2)\mid\ge{\delta}m$, where $\Delta$ denotes symmetric difference (the symmetric difference of two sets is the set of elements that is in exactly one of the two sets). Find the largest possible integer $s$ such that there exists an integer $m$ and a $\frac{1024}{2047}-good$ set of size $s$.