$R$, of which on lattices large enough to support non–perturbative physics there are typically a very large number [@hart97a]. These correspond to the (lattice) Gribov copies. Gauge dependent quantities appear to vary by ${\cal O}(10\%)$ depending upon the Gribov copy chosen; this is true not only of local quantities such as the magnetic current density [@hioki91] but also of supposedly long range, physical numbers such as the Abelian and monopole string tensions [@bali96; @hart97a]. Some criterion must be employed for the selection of the maxima of $R$, and in the absence of a clear understanding of which maximum, if any, is the most ‘physical’, one maximum was selected at random in [@hart98]. An alternative strategy, used in gauge fixing the $L=32$ lattices at $\beta = 2.5115$, is to pursue the global maximum of $R$ [@bali96]. Each field configuration is fixed to the maximally Abelian gauge 10 times using a simulated annealing algorithm that already weights the distribution of maxima so selected towards those of higher $R$. The solution with the largest $R$ from these is selected. Details of this method are discussed in [@bali96]. The difference in procedures invites caution in comparing exact numbers between this ensemble and those studied 