  An optimization for multilayered nanotubes that minimizes the scattering
efficiency for a given polarization is derived. The cylindrical nanocavities
have a radially periodic distribution, and the marginal layers that play a
crucial role particularly in the presence of nonlocalities are disposed to
reduce the scattering efficiency up to two orders of magnitude in comparison
with previous proposals. The predominant causes leading to such invisibility
effect are critically discussed. A transfer-matrix formalism is additionally
developed for the fast estimation of the scattering efficiency of the
nanostructures.
