  We present a theoretical discussion of a self-assembly scheme which makes it
possible to use DNA to uniquely encode the composition and structure of micro-
and nanoparticle clusters. These anisotropic DNA-decorated clusters can be
further used as building blocks for hierarchical self-assembly of larger
structures. We address several important aspects of possible experimental
implementation of the proposed scheme: the competition between different types
of clusters in a solution, possible jamming in an unwanted configuration, and
the degeneracy due to symmetry with respect to particle permutations.
