Convex sets of some doubly stochastic matrices

Let Ω denote the set of all n by n doubly stochastic matrices. Let t be a real number such that $\text{1}\text{t}\text{?}\text{1}\text{n}$ and let m be a real number such that $\text{1}\text{m}\text{? 1 ?}\text{1}\text{t}$. The set $\text{Ω}{}_{\mathrm{s}}\text{= {A ? Ω :}\text{1}\text{m}\text{? a}{}_{\mathrm{ij}}\text{?}\text{1}\text{t}\text{, 1 ? i, j ? n}}$ is the convex hull of the matrices in $\text{Ω}{}_{\mathrm{s}}$ having as many largest entries, namely, $\text{1}\text{t}$, as possible in each row and column while filling out the remaining entries with the value $\text{1}\text{m}$ and if necessary at most one entry in each row and column which has a value between $\text{1}\text{m}$ and $\text{1}\text{t}$.