AG(4,3): n points, the best layout found (a hyperplane, plus points in the two parallel ones) against the most the counting argument allows n= 3 built 1 proved at most 1 TIGHT (no split allowed; splits allowed: []) n= 4 built 1 proved at most 1 TIGHT (no split allowed; splits allowed: []) n= 5 built 2 proved at most 2 TIGHT (no split allowed; splits allowed: []) n= 6 built 3 proved at most 3 TIGHT (pairs alone (too many); splits allowed: [(2, 2, 2)]) n= 7 built 5 proved at most 5 TIGHT (no split allowed; splits allowed: []) n= 8 built 8 proved at most 8 TIGHT (no split allowed; splits allowed: []) n= 9 built 12 proved at most 12 TIGHT (no split allowed; splits allowed: []) n=10 built 12 proved at most 12 TIGHT (no split allowed; splits allowed: []) n=11 built 13 proved at most 13 TIGHT (pairs alone (too many); splits allowed: [(4, 4, 3)]) n=12 built 14 proved at most 14 TIGHT (pairs alone (too many); splits allowed: [(4, 4, 4), (5, 4, 3)]) n=13 built 16 proved at most 16 TIGHT (pairs alone (too many); splits allowed: [(5, 4, 4), (5, 5, 3), (6, 4, 3)]) n=14 built 19 proved at most 19 TIGHT (pairs alone (too many); splits allowed: [(5, 5, 4), (6, 4, 4), (6, 5, 3)]) n=15 built 23 proved at most 23 TIGHT (pairs alone (too many); splits allowed: [(5, 5, 5), (6, 5, 4), (6, 6, 3)]) n=16 built 26 proved at most 26 TIGHT (triples alone; splits allowed: [(6, 5, 5), (6, 6, 4), (7, 5, 4), (7, 6, 3)]) n=17 built 30 proved at most 30 TIGHT (triples alone; splits allowed: [(6, 6, 5), (7, 5, 5), (7, 6, 4), (7, 7, 3), (8, 5, 4)]) n=18 built 36 proved at most 36 TIGHT (pairs alone (too many); splits allowed: [(6, 6, 6), (7, 6, 5), (7, 7, 4), (8, 5, 5)]) n=19 built 41 proved at most 41 TIGHT (pairs alone (too many); splits allowed: [(7, 6, 6), (7, 7, 5), (8, 6, 5), (8, 7, 4)]) n=20 built 47 proved at most 47 TIGHT (triples alone; splits allowed: [(7, 7, 6), (8, 6, 6), (8, 7, 5), (8, 8, 4)]) n=21 built 54 proved at most 54 TIGHT (pairs alone (too many); splits allowed: [(7, 7, 7), (8, 7, 6), (8, 8, 5)]) n=22 built 62 proved at most 62 TIGHT (pairs alone (too many); splits allowed: [(8, 7, 7), (8, 8, 6)]) n=23 built 71 proved at most 71 TIGHT (pairs alone (too many); splits allowed: [(8, 8, 7)]) n=24 built 81 proved at most 81 TIGHT (pairs alone (too many); splits allowed: [(8, 8, 8)]) n=25 built 92 proved at most 92 TIGHT (no split allowed; splits allowed: []) n=26 built 104 proved at most 104 TIGHT (no split allowed; splits allowed: []) n=27 built 117 proved at most 117 TIGHT (no split allowed; splits allowed: []) n=28 built 117 proved at most 117 TIGHT (no split allowed; splits allowed: []) n=29 built 118 proved at most 118 TIGHT (pairs alone (too many); splits allowed: [(10, 10, 9)]) n=30 built 119 proved at most 119 TIGHT (pairs alone (too many); splits allowed: [(10, 10, 10), (11, 10, 9), (11, 11, 8)]) n=31 built 121 proved at most 121 TIGHT (pairs alone (too many); splits allowed: [(11, 10, 10), (11, 11, 9), (12, 10, 9), (12, 11, 8)]) n=32 built 124 proved at most 124 TIGHT (pairs alone (too many); splits allowed: [(11, 11, 10), (12, 10, 10), (12, 11, 9), (12, 12, 8), (13, 10, 9), (13, 11, 8)]) n=33 built 128 proved at most 128 TIGHT (triples alone; splits allowed: [(11, 11, 11), (12, 11, 10), (12, 12, 9), (13, 10, 10), (13, 11, 9), (13, 12, 8), (14, 10, 9)]) n=34 built 131 proved at most 131 TIGHT (both together; splits allowed: [(12, 11, 11), (12, 12, 10), (13, 11, 10), (13, 12, 9), (13, 13, 8), (14, 10, 10), (14, 11, 9), (14, 12, 8), (15, 10, 9), (15, 11, 8)]) n=35 built 135 proved at most 135 TIGHT (both together; splits allowed: [(12, 12, 11), (13, 11, 11), (13, 12, 10), (13, 13, 9), (14, 11, 10), (14, 12, 9), (14, 13, 8), (14, 14, 7), (15, 10, 10), (15, 11, 9), (15, 12, 8), (16, 10, 9)]) n=36 built 140 proved at most 140 TIGHT (both together; splits allowed: [(12, 12, 12), (13, 12, 11), (13, 13, 10), (14, 11, 11), (14, 12, 10), (14, 13, 9), (14, 14, 8), (15, 11, 10), (15, 12, 9), (15, 13, 8), (15, 14, 7), (16, 10, 10), (16, 11, 9), (16, 12, 8), (17, 10, 9), (18, 9, 9)]) n=37 built 146 proved at most 146 TIGHT (both together; splits allowed: [(13, 12, 12), (13, 13, 11), (14, 12, 11), (14, 13, 10), (14, 14, 9), (15, 11, 11), (15, 12, 10), (15, 13, 9), (15, 14, 8), (15, 15, 7), (16, 11, 10), (16, 12, 9), (16, 13, 8), (16, 14, 7), (17, 10, 10), (17, 11, 9), (17, 12, 8), (18, 10, 9)]) n=38 built 152 proved at most 152 TIGHT (both together; splits allowed: [(13, 13, 12), (14, 12, 12), (14, 13, 11), (14, 14, 10), (15, 12, 11), (15, 13, 10), (15, 14, 9), (15, 15, 8), (16, 11, 11), (16, 12, 10), (16, 13, 9), (16, 14, 8), (16, 15, 7), (17, 11, 10), (17, 12, 9), (17, 13, 8), (18, 10, 10), (18, 11, 9), (18, 12, 8), (19, 10, 9)]) n=39 built 159 proved at most 159 TIGHT (both together; splits allowed: [(13, 13, 13), (14, 13, 12), (14, 14, 11), (15, 12, 12), (15, 13, 11), (15, 14, 10), (15, 15, 9), (16, 12, 11), (16, 13, 10), (16, 14, 9), (16, 15, 8), (16, 16, 7), (17, 11, 11), (17, 12, 10), (17, 13, 9), (17, 14, 8), (17, 15, 7), (18, 11, 10), (18, 12, 9), (18, 13, 8), (19, 10, 10), (19, 11, 9), (20, 10, 9)]) n=40 built 167 proved at most 167 TIGHT (both together; splits allowed: [(14, 13, 13), (14, 14, 12), (15, 13, 12), (15, 14, 11), (15, 15, 10), (16, 12, 12), (16, 13, 11), (16, 14, 10), (16, 15, 9), (16, 16, 8), (17, 12, 11), (17, 13, 10), (17, 14, 9), (17, 15, 8), (17, 16, 7), (18, 11, 11), (18, 12, 10), (18, 13, 9), (18, 14, 8), (18, 15, 7), (19, 11, 10), (19, 12, 9), (19, 13, 8), (20, 10, 10), (20, 11, 9), (21, 10, 9)]) n=41 built 176 proved at most 176 TIGHT (both together; splits allowed: [(14, 14, 13), (15, 13, 13), (15, 14, 12), (15, 15, 11), (16, 13, 12), (16, 14, 11), (16, 15, 10), (16, 16, 9), (17, 12, 12), (17, 13, 11), (17, 14, 10), (17, 15, 9), (17, 16, 8), (17, 17, 7), (18, 12, 11), (18, 13, 10), (18, 14, 9), (18, 15, 8), (18, 16, 7), (19, 11, 11), (19, 12, 10), (19, 13, 9), (19, 14, 8), (20, 11, 10), (20, 12, 9), (21, 10, 10), (21, 11, 9)]) n=42 built 186 proved at most 186 TIGHT (both together; splits allowed: [(14, 14, 14), (15, 14, 13), (15, 15, 12), (16, 13, 13), (16, 14, 12), (16, 15, 11), (16, 16, 10), (17, 13, 12), (17, 14, 11), (17, 15, 10), (17, 16, 9), (17, 17, 8), (18, 12, 12), (18, 13, 11), (18, 14, 10), (18, 15, 9), (18, 16, 8), (18, 17, 7), (19, 12, 11), (19, 13, 10), (19, 14, 9), (19, 15, 8), (20, 11, 11), (20, 12, 10), (20, 13, 9), (21, 11, 10), (21, 12, 9)]) n=43 built 197 proved at most 197 TIGHT (both together; splits allowed: [(15, 14, 14), (15, 15, 13), (16, 14, 13), (16, 15, 12), (16, 16, 11), (17, 13, 13), (17, 14, 12), (17, 15, 11), (17, 16, 10), (17, 17, 9), (18, 13, 12), (18, 14, 11), (18, 15, 10), (18, 16, 9), (18, 17, 8), (18, 18, 7), (19, 12, 12), (19, 13, 11), (19, 14, 10), (19, 15, 9), (19, 16, 8), (20, 12, 11), (20, 13, 10), (20, 14, 9), (20, 15, 8), (21, 11, 11), (21, 12, 10), (21, 13, 9)]) n=44 built 209 proved at most 209 TIGHT (both together; splits allowed: [(15, 15, 14), (16, 14, 14), (16, 15, 13), (16, 16, 12), (17, 14, 13), (17, 15, 12), (17, 16, 11), (17, 17, 10), (18, 13, 13), (18, 14, 12), (18, 15, 11), (18, 16, 10), (18, 17, 9), (18, 18, 8), (19, 13, 12), (19, 14, 11), (19, 15, 10), (19, 16, 9), (19, 17, 8), (20, 12, 12), (20, 13, 11), (20, 14, 10), (20, 15, 9), (21, 12, 11), (21, 13, 10), (21, 14, 9)]) n=45 built 222 proved at most 222 TIGHT (both together; splits allowed: [(15, 15, 15), (16, 15, 14), (16, 16, 13), (17, 14, 14), (17, 15, 13), (17, 16, 12), (17, 17, 11), (18, 14, 13), (18, 15, 12), (18, 16, 11), (18, 17, 10), (18, 18, 9), (19, 13, 13), (19, 14, 12), (19, 15, 11), (19, 16, 10), (19, 17, 9), (19, 18, 8), (20, 13, 12), (20, 14, 11), (20, 15, 10), (20, 16, 9), (21, 12, 12), (21, 13, 11), (21, 14, 10), (21, 15, 9)]) n=46 built 231 proved at most 231 TIGHT (both together; splits allowed: [(16, 15, 15), (16, 16, 14), (17, 15, 14), (17, 16, 13), (17, 17, 12), (18, 14, 14), (18, 15, 13), (18, 16, 12), (18, 17, 11), (18, 18, 10), (19, 14, 13), (19, 15, 12), (19, 16, 11), (19, 17, 10), (19, 18, 9), (19, 19, 8), (20, 13, 13), (20, 14, 12), (20, 15, 11), (20, 16, 10), (20, 17, 9), (20, 18, 8), (21, 13, 12), (21, 14, 11), (21, 15, 10), (21, 16, 9), (22, 12, 12), (22, 13, 11), (22, 14, 10), (22, 15, 9)]) n=47 built 241 proved at most 241 TIGHT (both together; splits allowed: [(16, 16, 15), (17, 15, 15), (17, 16, 14), (17, 17, 13), (18, 15, 14), (18, 16, 13), (18, 17, 12), (18, 18, 11), (19, 14, 14), (19, 15, 13), (19, 16, 12), (19, 17, 11), (19, 18, 10), (19, 19, 9), (20, 14, 13), (20, 15, 12), (20, 16, 11), (20, 17, 10), (20, 18, 9), (20, 19, 8), (21, 13, 13), (21, 14, 12), (21, 15, 11), (21, 16, 10), (21, 17, 9), (21, 18, 8), (22, 13, 12), (22, 14, 11), (22, 15, 10), (22, 16, 9), (23, 12, 12), (23, 13, 11), (23, 14, 10)]) n=48 built 252 proved at most 253 gap 1 (both together; splits allowed: [(16, 16, 16), (17, 16, 15), (17, 17, 14), (18, 15, 15), (18, 16, 14), (18, 17, 13), (18, 18, 12), (19, 15, 14), (19, 16, 13), (19, 17, 12), (19, 18, 11), (19, 19, 10), (20, 14, 14), (20, 15, 13), (20, 16, 12), (20, 17, 11), (20, 18, 10), (20, 19, 9), (20, 20, 8), (21, 14, 13), (21, 15, 12), (21, 16, 11), (21, 17, 10), (21, 18, 9), (21, 19, 8), (22, 13, 13), (22, 14, 12), (22, 15, 11), (22, 16, 10), (22, 17, 9), (23, 13, 12), (23, 14, 11), (23, 15, 10)]) n=49 built 264 proved at most 267 gap 3 (both together; splits allowed: [(17, 16, 16), (17, 17, 15), (18, 16, 15), (18, 17, 14), (18, 18, 13), (19, 15, 15), (19, 16, 14), (19, 17, 13), (19, 18, 12), (19, 19, 11), (20, 15, 14), (20, 16, 13), (20, 17, 12), (20, 18, 11), (20, 19, 10), (20, 20, 9), (21, 14, 14), (21, 15, 13), (21, 16, 12), (21, 17, 11), (21, 18, 10), (21, 19, 9), (21, 20, 8), (22, 14, 13), (22, 15, 12), (22, 16, 11), (22, 17, 10), (22, 18, 9), (23, 13, 13), (23, 14, 12), (23, 15, 11), (23, 16, 10)]) n=50 built 276 proved at most 281 gap 5 (both together; splits allowed: [(17, 17, 16), (18, 16, 16), (18, 17, 15), (18, 18, 14), (19, 16, 15), (19, 17, 14), (19, 18, 13), (19, 19, 12), (20, 15, 15), (20, 16, 14), (20, 17, 13), (20, 18, 12), (20, 19, 11), (20, 20, 10), (21, 15, 14), (21, 16, 13), (21, 17, 12), (21, 18, 11), (21, 19, 10), (21, 20, 9), (21, 21, 8), (22, 14, 14), (22, 15, 13), (22, 16, 12), (22, 17, 11), (22, 18, 10), (22, 19, 9), (23, 14, 13), (23, 15, 12), (23, 16, 11), (23, 17, 10), (24, 13, 13), (24, 14, 12), (24, 15, 11)]) n=51 built 289 proved at most 295 gap 6 (both together; splits allowed: [(17, 17, 17), (18, 17, 16), (18, 18, 15), (19, 16, 16), (19, 17, 15), (19, 18, 14), (19, 19, 13), (20, 16, 15), (20, 17, 14), (20, 18, 13), (20, 19, 12), (20, 20, 11), (21, 15, 15), (21, 16, 14), (21, 17, 13), (21, 18, 12), (21, 19, 11), (21, 20, 10), (21, 21, 9), (22, 15, 14), (22, 16, 13), (22, 17, 12), (22, 18, 11), (22, 19, 10), (22, 20, 9), (23, 14, 14), (23, 15, 13), (23, 16, 12), (23, 17, 11), (23, 18, 10), (24, 14, 13), (24, 15, 12), (24, 16, 11)]) n=52 built 303 proved at most 309 gap 6 (both together; splits allowed: [(18, 17, 17), (18, 18, 16), (19, 17, 16), (19, 18, 15), (19, 19, 14), (20, 16, 16), (20, 17, 15), (20, 18, 14), (20, 19, 13), (20, 20, 12), (21, 16, 15), (21, 17, 14), (21, 18, 13), (21, 19, 12), (21, 20, 11), (21, 21, 10), (22, 15, 15), (22, 16, 14), (22, 17, 13), (22, 18, 12), (22, 19, 11), (22, 20, 10), (22, 21, 9), (23, 15, 14), (23, 16, 13), (23, 17, 12), (23, 18, 11), (23, 19, 10), (23, 20, 9), (24, 14, 14), (24, 15, 13), (24, 16, 12), (24, 17, 11)]) n=53 built 318 proved at most 326 gap 8 (both together; splits allowed: [(18, 18, 17), (19, 17, 17), (19, 18, 16), (19, 19, 15), (20, 17, 16), (20, 18, 15), (20, 19, 14), (20, 20, 13), (21, 16, 16), (21, 17, 15), (21, 18, 14), (21, 19, 13), (21, 20, 12), (21, 21, 11), (22, 16, 15), (22, 17, 14), (22, 18, 13), (22, 19, 12), (22, 20, 11), (22, 21, 10), (22, 22, 9), (23, 15, 15), (23, 16, 14), (23, 17, 13), (23, 18, 12), (23, 19, 11), (23, 20, 10), (24, 15, 14), (24, 16, 13), (24, 17, 12), (24, 18, 11)]) n=54 built 334 proved at most 344 gap 10 (both together; splits allowed: [(18, 18, 18), (19, 18, 17), (19, 19, 16), (20, 17, 17), (20, 18, 16), (20, 19, 15), (20, 20, 14), (21, 17, 16), (21, 18, 15), (21, 19, 14), (21, 20, 13), (21, 21, 12), (22, 16, 16), (22, 17, 15), (22, 18, 14), (22, 19, 13), (22, 20, 12), (22, 21, 11), (22, 22, 10), (23, 16, 15), (23, 17, 14), (23, 18, 13), (23, 19, 12), (23, 20, 11), (23, 21, 10), (24, 15, 15), (24, 16, 14), (24, 17, 13), (24, 18, 12)]) n=55 built 351 proved at most 360 gap 9 (both together; splits allowed: [(19, 18, 18), (19, 19, 17), (20, 18, 17), (20, 19, 16), (20, 20, 15), (21, 17, 17), (21, 18, 16), (21, 19, 15), (21, 20, 14), (21, 21, 13), (22, 17, 16), (22, 18, 15), (22, 19, 14), (22, 20, 13), (22, 21, 12), (22, 22, 11), (23, 16, 16), (23, 17, 15), (23, 18, 14), (23, 19, 13), (23, 20, 12), (23, 21, 11), (23, 22, 10), (23, 23, 9), (24, 16, 15), (24, 17, 14), (24, 18, 13), (24, 19, 12), (24, 20, 11), (25, 15, 15), (25, 16, 14)]) n=56 built 369 proved at most 376 gap 7 (both together; splits allowed: [(19, 19, 18), (20, 18, 18), (20, 19, 17), (20, 20, 16), (21, 18, 17), (21, 19, 16), (21, 20, 15), (21, 21, 14), (22, 17, 17), (22, 18, 16), (22, 19, 15), (22, 20, 14), (22, 21, 13), (22, 22, 12), (23, 17, 16), (23, 18, 15), (23, 19, 14), (23, 20, 13), (23, 21, 12), (23, 22, 11), (23, 23, 10), (24, 16, 16), (24, 17, 15), (24, 18, 14), (24, 19, 13), (24, 20, 12), (24, 21, 11), (25, 16, 15), (25, 17, 14), (25, 18, 13)]) n=57 built 388 proved at most 396 gap 8 (both together; splits allowed: [(19, 19, 19), (20, 19, 18), (20, 20, 17), (21, 18, 18), (21, 19, 17), (21, 20, 16), (21, 21, 15), (22, 18, 17), (22, 19, 16), (22, 20, 15), (22, 21, 14), (22, 22, 13), (23, 17, 17), (23, 18, 16), (23, 19, 15), (23, 20, 14), (23, 21, 13), (23, 22, 12), (23, 23, 11), (24, 17, 16), (24, 18, 15), (24, 19, 14), (24, 20, 13), (24, 21, 12), (24, 22, 11), (25, 16, 16), (25, 17, 15), (25, 18, 14)]) n=58 built 406 proved at most 412 gap 6 (both together; splits allowed: [(20, 19, 19), (20, 20, 18), (21, 19, 18), (21, 20, 17), (21, 21, 16), (22, 18, 18), (22, 19, 17), (22, 20, 16), (22, 21, 15), (22, 22, 14), (23, 18, 17), (23, 19, 16), (23, 20, 15), (23, 21, 14), (23, 22, 13), (23, 23, 12), (24, 17, 17), (24, 18, 16), (24, 19, 15), (24, 20, 14), (24, 21, 13), (24, 22, 12), (24, 23, 11), (24, 24, 10), (25, 17, 16), (25, 18, 15), (25, 19, 14), (25, 20, 13)]) n=59 built 425 proved at most 432 gap 7 (both together; splits allowed: [(20, 20, 19), (21, 19, 19), (21, 20, 18), (21, 21, 17), (22, 19, 18), (22, 20, 17), (22, 21, 16), (22, 22, 15), (23, 18, 18), (23, 19, 17), (23, 20, 16), (23, 21, 15), (23, 22, 14), (23, 23, 13), (24, 18, 17), (24, 19, 16), (24, 20, 15), (24, 21, 14), (24, 22, 13), (24, 23, 12), (24, 24, 11), (25, 17, 17), (25, 18, 16), (25, 19, 15), (25, 20, 14), (25, 21, 13), (26, 18, 15)]) n=60 built 446 proved at most 454 gap 8 (both together; splits allowed: [(20, 20, 20), (21, 20, 19), (21, 21, 18), (22, 19, 19), (22, 20, 18), (22, 21, 17), (22, 22, 16), (23, 19, 18), (23, 20, 17), (23, 21, 16), (23, 22, 15), (23, 23, 14), (24, 18, 18), (24, 19, 17), (24, 20, 16), (24, 21, 15), (24, 22, 14), (24, 23, 13), (24, 24, 12), (25, 18, 17), (25, 19, 16), (25, 20, 15), (25, 21, 14), (25, 22, 13)])