  This paper considers the degree-diameter problem for undirected circulant
graphs. For degrees 10 and 11 newly discovered families of circulant graphs of
arbitrary diameter are presented which are largest known and are conjectured to
be extremal. They are also the largest-known Abelian Cayley graphs of these
degrees. For each such family the order of every graph in the family is defined
by a quintic polynomial function of the diameter which is specific to the
family. The elements of the generating set for each graph are similarly defined
by a set of polynomials in the diameter. The existence of the graphs in the
degree 10 families has been proved for all diameters. These graphs are
consistent with a conjecture on the order of extremal Abelian Cayley and
circulant graphs of any degree and diameter.
  This is the extended version of the paper, including the proof steps for
degree 10 graphs covering all diameter classes and an appendix listing
additional tables of generating sets.
