Roughly speaking, in the implementation by Frühbis-Krüger/Pfister the centers are chosen as follows: Set
The locus where nd is attained is contained in a smooth hypersurface Z which "behaves well" w.r.t. intersecting the exceptional locus.
Now, intersect with Z (some modifications needed to
avoid certain bad points) and proceed as above, until
one gets a smooth hypersurface inside
The latter is returned as center.
