In this paper, locally asymptotically optimal (in the Hajek-Le Cam sense) parametric, pseudo-Gaussian and rank-based procedures are proposed for the problem of testing randomness against first-order superdiagonal bilinear panel dependence (in large n and small T panels). Local powers and asymptotic relative efficiencies are computed and show that the van der Waerden version of our rank-based tests uniformly dominates. Small-sample performances are investigated via simulations and confirm the theoretical findings, they also demonstrate the remarkable performances of rank procedures based on data-driven scores.