quadric grids (a,b), 0<=a,b<=6: configurations 48 | gap 1: 3 (coplanar 3, pseudostar 0, OTHER 0) | coplanar/pseudostar without gap 1: 0 | ACM tested 48: non-ACM 30 (connected 20), non-ACM with gap 1: 0, gap-1 and non-ACM: 0 | max regularity - s: 0 | gaps {1: 3, 2: 45}
   ACM iff |a-b| <= 1: violations [] ; gap-1 grids: [(0, 1), (1, 0), (1, 1)]
27 lines of the Fermat cubic: every line meets {10} others; alpha=3; dim I^(2) in degree alpha+1 = 0; alpha(I^(2)) = 6
27 lines: all subsets of size <= 4: configurations 20853 | gap 1: 207 (coplanar 207, pseudostar 0, OTHER 0) | coplanar/pseudostar without gap 1: 0 | ACM tested 20853: non-ACM 17406 (connected 6480), non-ACM with gap 1: 0, gap-1 and non-ACM: 0 | max regularity - s: 0 | gaps {1: 207, 2: 19566, 3: 1080}
   a double-six: ((0, 4, 8, 10, 14, 15), (1, 5, 6, 9, 13, 17))
27 lines: 2500 random subsets of size 5..27, a six, a double-six and its complement: configurations 2503 | gap 1: 0 (coplanar 0, pseudostar 0, OTHER 0) | coplanar/pseudostar without gap 1: 0 | gaps {3: 3}
   six: s=6 alpha=3 alpha2=6 ACM=False rao=[5, 8, 8, 5]
   double-six: s=12 alpha=3 alpha2=6 ACM=True rao=[0, 0, 0, 0, 0]
   complement of the double-six: s=15 alpha=3 alpha2=6 ACM=True rao=[0, 0, 0, 0, 0, 0]
Reye 16 lines: s=16 alpha=4 alpha2=8 gap1=False kind=other ACM=True rao=[0, 0, 0, 0, 0, 0]
edges of two desmic tetrahedra: s=12 alpha=4 alpha2=6 gap1=False kind=other ACM=True rao=[0, 0, 0, 0]
edges of three desmic tetrahedra: s=18 alpha=6 alpha2=10 gap1=False kind=other ACM=False rao=[0, 0, 0, 4, 7, 4]
arrangement A_4 (10 planes): 25 lines on >= 2 planes; multiplicities {2: 15, 3: 10}
arrangement D_4 (12 planes): 34 lines on >= 2 planes; multiplicities {2: 18, 3: 16}
arrangement B_4 (16 planes): 58 lines on >= 2 planes; multiplicities {2: 36, 3: 16, 4: 6}
arrangement A_3 x A_1 (7 planes: x_i = x_j for i<j<=4 in P^3 = P(k^4), and x_4 = 0): 13 lines on >= 2 planes; multiplicities {2: 9, 3: 4}
   A_4 (10 planes) / all lines on >=2 planes: s=25 alpha=6 gap1=False alpha2=10 kind=other ACM=True
   A_4 (10 planes) / lines on >=3 planes: s=10 alpha=4 gap1=False alpha2=8 kind=other ACM=True
   A_4 (10 planes) / lines on exactly 2 planes: s=15 alpha=5 gap1=False alpha2=8 kind=other ACM=True
   D_4 (12 planes) / all lines on >=2 planes: s=34 alpha=7 gap1=False alpha2=12 kind=other ACM=None
   D_4 (12 planes) / lines on >=3 planes: s=16 alpha=4 gap1=False alpha2=8 kind=other ACM=None
   D_4 (12 planes) / lines on exactly 2 planes: s=18 alpha=6 gap1=False alpha2=10 kind=other ACM=None
   B_4 (16 planes) / all lines on >=2 planes: s=58 alpha=9 gap1=False alpha2=None kind=other ACM=None
   B_4 (16 planes) / lines on >=3 planes: s=22 alpha=6 gap1=False alpha2=None kind=other ACM=None
   B_4 (16 planes) / lines on exactly 2 planes: s=36 alpha=8 gap1=False alpha2=None kind=other ACM=None
   A_3 x A_1 (7 planes: x_i = x_j for i<j<=4 in P^3 = P(k^4), and x_4 = 0) / all lines on >=2 planes: s=13 alpha=4 gap1=False alpha2=7 kind=other ACM=True
   A_3 x A_1 (7 planes: x_i = x_j for i<j<=4 in P^3 = P(k^4), and x_4 = 0) / lines on >=3 planes: s=4 alpha=2 gap1=False alpha2=4 kind=other ACM=True
   A_3 x A_1 (7 planes: x_i = x_j for i<j<=4 in P^3 = P(k^4), and x_4 = 0) / lines on exactly 2 planes: s=9 alpha=3 gap1=False alpha2=5 kind=other ACM=True
reflection arrangements: configurations 12 | gap 1: 0 (coplanar 0, pseudostar 0, OTHER 0) | coplanar/pseudostar without gap 1: 0 | ACM tested 6: non-ACM 0 (connected 0), non-ACM with gap 1: 0, gap-1 and non-ACM: 0 | max regularity - s: -1 | gaps {2: 2, 3: 2, 4: 4, 5: 1}
PG(3,3): 130 lines; W(3): 40 totally isotropic lines; regular spread: 10 lines, pairwise skew: True
   W(3), 40 lines: s=40 alpha=4 gap1=False alpha2=None kind=other ACM=None rao=None
   regular spread of PG(3,3), 10 lines: s=10 alpha=4 gap1=False alpha2=8 kind=other ACM=False rao=[9, 16, 20, 20, 17, 12, 8, 4, 2]
   all 130 lines of PG(3,3): s=130 alpha=13 gap1=False alpha2=None kind=other ACM=None rao=None
random / incidence-rich configurations in PG(3,3): configurations 5998 | gap 1: 1025 (coplanar 590, pseudostar 435, OTHER 0) | coplanar/pseudostar without gap 1: 0 | ACM tested 4193: non-ACM 1836 (connected 823), non-ACM with gap 1: 0, gap-1 and non-ACM: 0 | max regularity - s: 0
   sizes {2: 525, 3: 583, 4: 540, 5: 795, 6: 622, 7: 703, 8: 425, 9: 609, 10: 464, 11: 181, 12: 181, 13: 76, 14: 186, 15: 54, 16: 54}
random / incidence-rich configurations in PG(3,5): configurations 3000 | gap 1: 439 (coplanar 200, pseudostar 239, OTHER 0) | coplanar/pseudostar without gap 1: 0 | ACM tested 2004: non-ACM 1090 (connected 314), non-ACM with gap 1: 0, gap-1 and non-ACM: 0 | max regularity - s: 0
   sizes {2: 243, 3: 243, 4: 259, 5: 375, 6: 316, 7: 364, 8: 204, 9: 325, 10: 235, 11: 107, 12: 60, 13: 19, 14: 125, 15: 51, 16: 74}
random / incidence-rich configurations in PG(3,7): configurations 3000 | gap 1: 465 (coplanar 192, pseudostar 273, OTHER 0) | coplanar/pseudostar without gap 1: 0 | ACM tested 1967: non-ACM 1127 (connected 296), non-ACM with gap 1: 0, gap-1 and non-ACM: 0 | max regularity - s: 0
   sizes {2: 243, 3: 270, 4: 241, 5: 386, 6: 323, 7: 323, 8: 181, 9: 316, 10: 260, 11: 123, 12: 43, 13: 24, 14: 134, 15: 53, 16: 80}
survey2 finished in 21s
