A computer search of maximal partial spreads in PG(3,q)

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 $q=7$.Comment: 10 page

New results on maximal partial line spreads in PG(5,q)

In this work, we prove the existence of maximal partial line spreads in PG(5,q) of size q^3+q^2+kq+1, with 1 \leq k \leq (q^3-q^2)/(q+1), k an integer. Moreover, by a computer search, we do this for larger values of k, for q \leq 7. Again by a computer search, we find the sizes for the largest maximal partial line spreads and many new results for q \leq 5

A new class of maximal partial spreads in PG(4,q)

In this work we construct a new class of maximal partial spreads in $PG(4,q)$, that we call $q$-added maximal partial spreads. We obtain them by depriving a spread of a hyperplane of some lines and adding $q+1$ lines not of the hyperplane for each removed line. We do this in a theoretic way for every value of $q$, and by a computer search for $q$ an odd prime and $q \leq 13$. More precisely we prove that for every $q$ there are $q$-added maximal partial spreads from the size $q^2+q+1$ to the size $q^2+(q-1)q+1$, while by a computer search we get larger cardinalities.Comment: 17 page