A new attainable lower bound on the number of nodes in quadruple circulant networks

We consider the problem of maximization of the number of nodes for fixed degree and diameter of undirected circulant networks. The known lower bound on the maximum order of quadruple circulant networks is improved by $O(d^3)$ for any even diameter $d\equiv0\pmod4$. The family of circulant networks achieving the obtained estimate is found. As we conjecture, the found graphs are the largest circulants for the dimension four. Tab. 2, bibliogr. 9.