Abstract: Globally coupled maps (GCMs) are prototypical examples of high-dimensional dynamical systems. Interestingly, GCMs formed by an ensemble of weakly coupled identical chaotic units generically exhibit a hyperchaotic ?turbulent? state. A decade ago, Takeuchi et al. [Phys. Rev. Lett. 107, 124101 (2011)] theorized that in turbulent GCMs the largest Lyapunov exponent (LE), ?(N), depends logarithmically on the system size N: ????(N)?c/lnN. We revisit the problem and analyze, by means of analytical and numerical techniques, turbulent GCMs with positive multipliers to show that there is a remarkable lack of universality, in conflict with the previous prediction. In fact, we find a power-law scaling ????(N)?c/N?, where ? is a parameter-dependent exponent in the range 0

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