Le rang des tissus de Nakai

According to Alain H'enaut, a planar 4-web is called Nakai’s web if the cross-ratio of the tangents to the four foliations at each point is constant and if it has no hexagonal 3-subweb. We prove that Nakai’s webs have rank 0 or

1. We give examples with rank 1 and present a universal way to build such examples.