The number of points in a matroid with no n-point line as a minor

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For any positive integer l we prove that if M is a simple matroid with no (l+2)-point line as a minor and with sufficiently large rank, then |E(M)|≤ qʳ⁽ᵐ⁾-1q-1, where q is the largest prime power less than or equal to l. Equality is attained by projective geometries over GF(q).