  A set of orthogonal product states of a composite Hilbert space is genuinely
nonlocal if the states are locally indistinguishable across any bipartition. In
this work, we construct a minimal set of party asymmetry genuine nonlocal set
in arbitrary large dimensional composite quantum systems $C^d\otimes C^d\otimes
C^d$. We provide a local discriminating protocol by using a three qubit GHZ
state as a resource. On the contrary, we observe that single-copy of two qubit
Bell states provide no advantage for this discrimination task. Recently, Halder
et al. [Phys. Rev. Lett. 122, 040403 (2019)], proposed the concept of strong
nonlocality without entanglement and ask an open question whether there exist
an incomplete strong nonlocal set or not. In [Phys. Rev. A 102, 042228 (2020)],
an answer is provided by the authors. Here, we construct an incomplete party
asymmetry strong nonlocal set which is more stronger than the set constructed
in [Phys. Rev. A 102, 042228 (2020)] with respect to the consumption of
entanglement as a resource for their respective discrimination tasks.
