  The goal of this paper is to describe a theoretical construction of an
infinite collection of non-classical Schottky groups. We first show that there
are infinitely many non-classical noded Schottky groups on the boundary of
Schottky space, and we show that infinitely many of these are "sufficiently
complicated". We then show that every Schottky group in an appropriately
defined relative conical neighborhood of any sufficiently complicated noded
Schottky group is necessarily non-classical. Finally, we construct two
examples; the first is a noded Riemann surface of genus $3$ that cannot be
uniformized by any neoclassical Schottky group (i.e., classical noded Schottky
group); the second is an explicit example of a sufficiently complicated noded
Schottky group in genus $3$.
