  Let $k$ denote a field with nontrivial discrete valuation. We assume that $k$
is complete with perfect residue field. Let $G$ be the group of $k$-rational
points of a reductive, linear algebraic group defined over $k$. Let $\gg$
denote the Lie algebra of $G$. Fix $r \in \R$. Subject to some restrictions, we
show that the set of distinguished degenerate Moy-Prasad cosets of depth $r$
(up to an equivalence relation) parametrizes the nilpotent orbits in $\gg$.
