Raynaud vector bundles

We construct vector bundles $R_{\mu }^r$ on a smooth projective curve $X$ having the property that for all sheaves $E$ of slope $\mu$ and rank $r$ on $X$ we have an equivalence: $E$ is a semistable vector bundle $⟺$ $Hom(R_{\mu }^r,E)=0$. As a byproduct of our construction we obtain effective bounds on $r$ such that the linear system $\mathrm{\mid }R\cdot \mathrm{\Theta }\mathrm{\mid }$ has base points on the moduli space $U_X(r,r(g-1))$.