On isotropy fields of $\mathrm{Spin}(18)$-torsors

It is shown that any $18$-dimensional nondegenerate quadratic form of trivial discriminant and Clifford invariant acquires Witt index at least $5$ over some finite ground field extension of degree not divisible by $2^4$. On the basis of previous research, a general formula is also established for all possible similar statements for forms of arbitrary dimension.