If the "unit distance" corresponds to exactly two elements having exchanged positions, then the answer to [this question](https://mathoverflow.net/questions/137922/algorithm-for-low-discrepancy-sequence-of-hamilton-cycles-in-complete-graphs) may be in the line of what you are looking for.  
It contains code for determining the $k$th permutation and also discusses successive refinement of a set of permutations. 

More generally, you could look for Gray codes for permutations like e.g. [in this paper](http://jl.baril.u-bourgogne.fr/kcycles.pdf)