We prove that the Grassmannian of totally isotropic k-spaces of the polar
space associated to the unitary group SU2nβ(F) (nβN) has generating rank (k2nβ) when Fξ =F4β. We also reprove the main result of Blok [Blok2007], namely that
the Grassmannian of totally isotropic k-spaces associated to the symplectic
group Sp2nβ(F) has generating rank (k2nβ)β(kβ22nβ), when Char(F)ξ =2