In this article we construct maximal partial 2spreads in
$PG\left(8,q\right)$ of
deficiency
$\delta =\left(k1\right)\cdot {q}^{2}$,
where
$k\le {q}^{2}+q+1$
and
$\delta =k\cdot {q}^{2}+l\cdot \left({q}^{2}1\right)+1$,
where
$k+l\le {q}^{2}$
and
$\delta =\left(k+1\right)\cdot {q}^{2}+l\cdot \left({q}^{2}1\right)+m\cdot \left({q}^{2}2\right)+1$,
where
$k+l+m\le {q}^{2}$.
Using these results, we also construct maximal partial 2spreads in
$PG\left(3m1,q\right)$ of various
deficiencies for
$m\ge 4$.
