Small tight sets of hyperbolic quadrics

An x-tight set of a hyperbolic quadric Q ⁺(2n + 1, q) can be described as a set M of points with the property that the number of points of M in the tangent hyperplanes of points of M is as big as possible. We show that such a set is necessarily the union of x mutually disjoint generators provided that x ≤ q and n ≤ 3, or that x < q, n ≥ 4 and q ≥ 71. This unifies and generalizes many results on x-tight sets that are presently known, see (J Comb Theory Ser A 114(7):1293–1314 1], J Comb Des 16(4):342–349 5], Des Codes Cryptogr 50:187–201 4], Adv Geom 4(3):279–286 8], Bull Lond Math Soc 42(6):991–996 11]).