  Reeder and Yu have recently given a new construction of a class of
supercuspidal representations called epipelagic representations. We explicitly
calculate the Local Langlands Correspondence for certain families of epipelagic
representations of unitary groups, following the general construction of
Kaletha [Kal15]. The interesting feature of our computation is that we find
simplifications within L-packets of the two novel invariants introduced in
[Kal15], the toral invariant and the admissible L-embedding.
