The network scenario offers interesting new perspectives on the phenomenon of
quantum nonlocality. Notably, when considering networks with independent
sources, it is possible to demonstrate quantum nonlocality without the need for
measurements inputs, i.e. with all parties performing a fixed quantum
measurement. Here we aim to find minimal examples of this effect. Focusing on
the minimal case of the triangle network, we present examples involving output
cardinalities of 3β3β3 and 3β3β2. Finally, we discuss the prospects of
finding an example of quantum nonlocality in the triangle network with binary
outputs, and point out a connection to the Lovasz local lemma