Geometrical Bell inequalities for arbitrarily many qudits with different outcome strategies

Greenberger-Horne-Zeilinger states are intuitively known to be the most non-classical ones. They lead to the most radically nonclassical behavior of three or more entangled quantum subsystems. However, in case of two-dimensional systems, it has been shown that GHZ states lead to more robustness of Bell nonclassicality in case of geometrical inequalities than in case of Mermin inequalities. We investigate various strategies of constructing geometrical Bell inequalities (BIs) for GHZ states for any dimensionality of subsystems.