There are three different types of nondeterminism in quantum communication: i) \nqp-communication, ii) \qma-communication, and iii) \qcma-communication. In this \redout{paper} we show that multiparty \nqp-communication can be exponentially stronger than \qcma-communication. This also implies an exponential separation with respect to classical multiparty nondeterministic communication complexity. We argue that there exists a total function that is hard for \qcma-communication and easy for \nqp-communication. The proof of it involves an application of the pattern tensor method and a new lower bound for polynomial threshold degree. Another important consequence of this result is that nondeterministic rank can be exponentially lower than the discrepancy bound.