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In this work, we prove the existence of maximal partial line spreads inPG(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 \leq7. Again by a computer search, we find the sizes for the largest maximalpartial line spreads and many new results for q \leq 5.

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