Is there a way to compute the following nullity of multilinear maps? As it is different from any nullity I know of, I call it *bunnity* after myself:-)) If it already has a name, it be nice to know it. References are particularly appreciated.

Let $V$ be a $d$-dimensional vector space over a field $K$, $f:V^{\otimes n}\rightarrow K$ a multilinear map. We define the bunnity by

$Bun(f) = sup \{ \sum_{k=1}^n dim(U_k) \ | \ f(U_1\otimes U_2 \ldots \otimes U_n)=0\}$.

If $n=2$, the bunnity is nullity plus dimension. It is more complicated if $n\geq 3$. I expect that for $n=3$ or $n=4$, there should be an algorithm because the 3-subspace problem is finite, while the 4-subspace problem is tame. I would be pleasantly surprised if there is an algorithm for a general $n$.

**EDIT** I forgot to say what $U_i$ are. They are **non-zero** vector subspaces of $V$.