From a computer search, new minimum sizes for the maximal partial spreads in \(PG(3,q)\) have been obtained for \(q = 8, 9, 16\) and for every \(q\) such that \(25 \leq q \leq 101\). Furthermore, density results in the cases \(q = 8, 9, 16, 19, 23, 25, 27\) have been obtained. Finally, the already known exceptional size \(45\) for \(q = 7\) has been found again.