  In device-independent quantum information processing Bell inequalities are
not only used as detectors of nonlocality, but also as certificates of relevant
quantum properties. In order for these certificates to work, one very often
needs Bell inequalities that are maximally violated by specific quantum states.
Recently, in [A. Salavrakos et al., Phys. Rev. Lett. 119, 040402 (2017)] a
general class of Bell inequalities, with arbitrary numbers of measurements and
outcomes, has been designed, which are maximally violated by the maximally
entangled states of two quantum systems of arbitrary dimension. In this work,
we generalize these results to the multipartite scenario and obtain a general
class of Bell inequalities maximally violated by the
Greenberger-Horne-Zeilinger states of any number of parties and any local
dimension. We then derive analytically their maximal quantum and nonsignaling
values. We also obtain analytically the bound for detecting genuine nonlocality
and compute the fully local bound for a few exemplary cases. Moreover, we
consider the question of adapting this class of inequalities to partially
entangled GHZ-like states for some special cases of low dimension and small
number of parties. Through numerical methods, we find classes of inequalities
maximally violated by these partially entangled states.
