  We show that finding rank-$R$ decompositions of a 3D tensor, for $R\le 4$,
over a fixed finite field can be done in polynomial time. However, if some
cells in the tensor are allowed to have arbitrary values, then rank-2 is
NP-hard over the integers modulo 2. We also explore rank-1 decomposition of a
3D tensor and of a matrix where some cells are allowed to have arbitrary
values.
