  The complexities of self-dual normal bases, which are candidates for the
lowest complexity basis of some defined extensions, are determined with the
help of the number of all but the simple points in well chosen minimal
Besicovitch arrangements. In this article, these values are first compared with
the expected value of the number of all but the simple points in a minimal
randomly selected Besicovitch arrangement in F d 2 for the first 370 prime
numbers d. Then, particular minimal Besicovitch arrangements which share
several geometrical properties with the arrangements considered to determine
the complexity will be considered in two distinct cases.
