Maximal partial spreads and the modular n-queen problem II Original Research Article

We prove that if q + 1 ≡ 8 or 16 (mod 24) then, for any integer n in the interval (q2 + 1)/2 + 3 ⩽ n ⩽ (5q2 + 4q + 7)/8, there is a maximal partial spread of size n in PG(3, q).