AG(5,3): every n <= 27 holds at most G3[n] lines (no split allowed: 10, pairs alone (too many): 14, triples alone: 1)
AG(6,3): every n <= 27 holds at most G3[n] lines (no split allowed: 10, pairs alone (too many): 15)
  so, by the monotone pair count, every AG(d,3) with d >= 6 does too