Mappings with dilatation in Orlicz spaces

We prove openness and discreteness for nonconstant mappings belonging to $W^{1,n}_{loc} (\Omega,\mathbb{R}^n)\geq 3$, with dilatation in certain Orlicz spaces which are strictly larger then all $L^p_{loc}(\Omega), p>n-1$. This result contributes to decreasing the gap between known results and a conjecture of Iwaniec and \v{S}verák.