Doubts on the existence of an exponential bound were raised by Catterall et al. , who considered the behaviour of in . Their data (taken for ) were consistent with a leading factorial behaviour . The same scenario was favoured by de Bakker and Smit , who performed further investigations of . Subsequently, Ambjørn and Jurkiewicz  and Brügmann and Marinari  added further data points at and respectively. Their numerical results, as well as those by Catterall et al. , who employed an alternative method for measuring , favour the existence of an exponential bound, although they cannot claim to be conclusive.
There have also been theoretical arguments for the existence of an exponential bound, based on the proofs of such bounds for the counting of minimal geodesic ball coverings of Riemannian spaces of bounded geometry [68, 26], and the counting of discrete curvature assignments to unordered sets of bones .
© Max Planck Society and the author(s)