  In the theory of composites, hierarchical laminate microstructures are known
to often show optimal behavior. In this paper, their performance in the context
of the Hall effect is evaluated. Using numerical calculations, it is shown that
- despite the fact that they are the result of a simple layering process - they
can mimic the behavior of chain-mail-inspired composites, which exhibit a
sign-inversion of the effective Hall coefficient. To obtain such a hierarchical
laminate, a two-step strategy is used: In the first step, a rank-three laminate
with an effective $S$-tensor that has a sign-inverted trace is introduced. In
the second step, the final isotropic hierarchical laminate is obtained from the
rank-three laminate using an idea of Schulgasser's. As measured by the
conductivity contrast required for the inversion as well as by the modulus of
the obtained sign-inverted Hall coefficient, the identified hierarchical
laminate performs better than the previously studied chain-mail-inspired
composites.
