Minor Description
The index of the BKD tree already allows to know lower and upper bounds of values in a given dimension. However the actual range of values might be more narrow than what the index tells us, especially if splitting on one dimension reduces the range of values in at least one other dimension. For instance this tends to be the case with range fields: since we enforce that lower bounds are less than upper bounds, splitting on one dimension will also affect the range of values in the other dimension.
So I'm wondering whether we should store the actual range of values for each dimension in leaf blocks, this will hopefully allow to figure out that either none or all values match in a block without having to check them all.