  Searching for other participants is one of the most important operations in a
distributed system. We are interested in topologies in which it is possible to
route a packet in a fixed number of hops until it arrives at its destination.
Given a constant $d$, this paper introduces a new self-stabilizing protocol for
the $q$-ary $d$-dimensional de Bruijn graph ($q = \sqrt[d]{n}$) that is able to
route any search request in at most $d$ hops w.h.p., while significantly
lowering the node degree compared to the clique: We require nodes to have a
degree of $\mathcal O(\sqrt[d]{n})$, which is asymptotically optimal for a
fixed diameter $d$. The protocol keeps the expected amount of edge redirections
per node in $\mathcal O(\sqrt[d]{n})$, when the number of nodes in the system
increases by factor $2^d$. The number of messages that are periodically sent
out by nodes is constant.
