Abstract
We prove that a non-empty set L of at most q5+q4+q3+q2+q+1 lines of PG(n,q) with the properties that (1) every point of PG(n,q) is incident with either 0 or q+1 elements of L, (2) every plane of PG(n,q) is incident with either 0, 1 or q+1 elements of L, (3) every solid of PG(n,q) is incident with either 0, 1, q+1 or 2q+1 elements of L, and (4) every four-dimensional subspace of PG(n,q) is incident with at most q3−q2+4q elements of L is necessarily the set of lines of a split Cayley hexagon H(q) naturally embedded in PG(6,q).
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