  In this work we find new minimum sizes for the maximal partial spreads of
PG$(3,q)$, for $q=8,9,16$ and for every $q$ such that $25\leq q\leq 101$.
Furthermore, for $q=8,9,16,25$ and 27 we find all the unknown sizes between our
minimums and the value $q^{2}-q+2$. Moreover, we obtain density results also in
the cases $q=19$ and $q=23$, already studied but not yet completed. Finally, we
find the known exceptional size 45 for $q=7$.
