Suppose you have a function on a product of intervals
We have some reason to believe that possibly after some coordinate change the points that are some nice fraction of the way along each coordinate axis are of more interest than the points where the coordinates do not have such nice form
Here nice form means that they are a/b^d with b something small like 2 or 3. b is fixed at the initial step
This means we are exploring points that are halfway or a third of the way along the interval and then moving on to stepping by quarters or ninths and so on
The points we are exploring are grouped by the maximum power d when each of the (before transformation) coordinates are written as a/b^d in lowest terms, call this set of points G_d
If there are too many of these because the dimensionality of the box is large and/or b^d is large, we can impose some decimation so only approximately f(d) many points are emitted from G_d if for a particular d, |G_d| <= f(d), this filtering does not take place but because |G_d| grows so fast and the provided f(d) should have much slower growth the filtering will happen at some stage