The $m$-Invariant of Fields of Characteristic 2

We study the minimal dimension of a nonsingular anisotropic universal quadratic form over a field $F$ of $\mathrm{char}(F)=2$, which we call the ``$m$-invariant" of $F$. We show that every even number is the $m$-invariant of some field of characteristic 2, and consider cases when $u(F)$ and $m(F)$ are equal and when they are not.