Maximal partial line spreads of PG(3, q), q even

Abstract

Applying the representation of PG(3, q) over AG(2, q), [3], we construct a maximal partial line spread of PG(3, q), q = 2²ⁿ, n an integer, n≥1, of size q² = q + 2.  This size is the greatest known till now, except a sporadic case, found by O. Heden [2], for q = 7.