AG(3,3) from the 3x3 grid: proved maximum against the exhaustive count (third.c)
n= 3  exhaustive   1  proved at most   1  TIGHT  (no split allowed)
n= 4  exhaustive   1  proved at most   1  TIGHT  (no split allowed)
n= 5  exhaustive   2  proved at most   2  TIGHT  (no split allowed)
n= 6  exhaustive   3  proved at most   3  TIGHT  (pairs alone (too many))
n= 7  exhaustive   5  proved at most   5  TIGHT  (no split allowed)
n= 8  exhaustive   8  proved at most   8  TIGHT  (no split allowed)
n= 9  exhaustive  12  proved at most  12  TIGHT  (no split allowed)
n=10  exhaustive  12  proved at most  12  TIGHT  (no split allowed)
n=11  exhaustive  13  proved at most  13  TIGHT  (pairs alone (too many))
n=12  exhaustive  14  proved at most  14  TIGHT  (pairs alone (too many))
n=13  exhaustive  16  proved at most  16  TIGHT  (triples alone)
n=14  exhaustive  19  proved at most  19  TIGHT  (triples alone)
n=15  exhaustive  23  proved at most  23  TIGHT  (both together)
n=16  exhaustive  26  proved at most  26  TIGHT  (both together)
n=17  exhaustive  30  proved at most  30  TIGHT  (both together)
n=18  exhaustive  36  proved at most  36  TIGHT  (both together)
n=19  exhaustive  41  proved at most  41  TIGHT  (both together)
n=20  exhaustive  47  proved at most  47  TIGHT  (both together)
n=21  exhaustive  54  proved at most  54  TIGHT  (both together)
n=22  exhaustive  62  proved at most  62  TIGHT  (pairs alone (too many))
n=23  exhaustive  71  proved at most  71  TIGHT  (pairs alone (too many))
n=24  exhaustive  81  proved at most  81  TIGHT  (pairs alone (too many))
n=25  exhaustive  92  proved at most  92  TIGHT  (no split allowed)
n=26  exhaustive 104  proved at most 104  TIGHT  (no split allowed)
n=27  exhaustive 117  proved at most 117  TIGHT  (no split allowed)