I'm writing a UB Tree for fun using a Z Order Curve. It is currently capable of storing points in any number of dimensions and when queried it performs a naive search between two Z Indexes, filtering and discarding any false positives. I would like to implement BIGMIN and LITMAX to minimize the number of false positives that it traverses, but I can't seem to find any information on how to implement those in a way that does not limit my tree to storing two dimensional data. For example, both this whitepaper and this blog post describe their implementation in terms that are heavily tied to working with 2D values.
Is there a dimensionality-agnostic way to implement this functionality?
For 2 dimension you can treat the z curve as a base-4 number (quadkey). IMO when you sort the quadkey from left to right it is similar to litmin and bigmin. For n-dimension treat it like a base-n number.