Maximal partial line spreads of non-singular quadrics

For n ≥ 9, we construct maximal partial line spreads for non-singular quadrics of PG(n, q) for every size between approximately (cn + d)(qn−3 + qn−5) log 2q and qn−2, for some small constants c and d. These results are similar to spectrum results on maximal partial line spreads in finite projective spaces by Heden, and by Gács and Szőnyi. These results also extend spectrum results on maximal partial line spreads in the finite generalized quadrangles W3(q) and Q(4, q) by Pepe, Rößing and Storme.