d | smax=(d-1)(d-2)/2 | C(d+1,3) | C(d+1,3) - smax*(d-1) | least s with s*(d-1) >= C(d+1,3)
 2 |   0 |    1 |     1 | 1   <- count suffices (difference > 0)
 3 |   1 |    4 |     2 | 2   <- count suffices (difference > 0)
 4 |   3 |   10 |     1 | 4   <- count suffices (difference > 0)
 5 |   6 |   20 |    -4 | 5   <- count fails for 5 <= s <= 6
 6 |  10 |   35 |   -15 | 7   <- count fails for 7 <= s <= 10
 7 |  15 |   56 |   -34 | 10   <- count fails for 10 <= s <= 15
 8 |  21 |   84 |   -63 | 12   <- count fails for 12 <= s <= 21
 9 |  28 |  120 |  -104 | 15   <- count fails for 15 <= s <= 28
10 |  36 |  165 |  -159 | 19   <- count fails for 19 <= s <= 36

random lines over F_p, p = 2^31-1: Hilbert function in degree d-2 (number of conditions imposed on forms of degree d-2)
  d=5 s= 1: HF_L(d-2) =   4 = min(s(d-1), C(d+1,3)) =   4 : True ; forms of degree d-2 through L: 16
  d=5 s= 2: HF_L(d-2) =   8 = min(s(d-1), C(d+1,3)) =   8 : True ; forms of degree d-2 through L: 12
  d=5 s= 3: HF_L(d-2) =  12 = min(s(d-1), C(d+1,3)) =  12 : True ; forms of degree d-2 through L: 8
  d=5 s= 4: HF_L(d-2) =  16 = min(s(d-1), C(d+1,3)) =  16 : True ; forms of degree d-2 through L: 4
  d=5 s= 5: HF_L(d-2) =  20 = min(s(d-1), C(d+1,3)) =  20 : True ; forms of degree d-2 through L: 0
  d=5 s= 6: HF_L(d-2) =  20 = min(s(d-1), C(d+1,3)) =  20 : True ; forms of degree d-2 through L: 0
  d=6 s= 1: HF_L(d-2) =   5 = min(s(d-1), C(d+1,3)) =   5 : True ; forms of degree d-2 through L: 30
  d=6 s= 2: HF_L(d-2) =  10 = min(s(d-1), C(d+1,3)) =  10 : True ; forms of degree d-2 through L: 25
  d=6 s= 3: HF_L(d-2) =  15 = min(s(d-1), C(d+1,3)) =  15 : True ; forms of degree d-2 through L: 20
  d=6 s= 4: HF_L(d-2) =  20 = min(s(d-1), C(d+1,3)) =  20 : True ; forms of degree d-2 through L: 15
  d=6 s= 5: HF_L(d-2) =  25 = min(s(d-1), C(d+1,3)) =  25 : True ; forms of degree d-2 through L: 10
  d=6 s= 6: HF_L(d-2) =  30 = min(s(d-1), C(d+1,3)) =  30 : True ; forms of degree d-2 through L: 5
  d=6 s= 7: HF_L(d-2) =  35 = min(s(d-1), C(d+1,3)) =  35 : True ; forms of degree d-2 through L: 0
  d=6 s= 8: HF_L(d-2) =  35 = min(s(d-1), C(d+1,3)) =  35 : True ; forms of degree d-2 through L: 0
  d=6 s= 9: HF_L(d-2) =  35 = min(s(d-1), C(d+1,3)) =  35 : True ; forms of degree d-2 through L: 0
  d=6 s=10: HF_L(d-2) =  35 = min(s(d-1), C(d+1,3)) =  35 : True ; forms of degree d-2 through L: 0
  d=7 s= 1: HF_L(d-2) =   6 = min(s(d-1), C(d+1,3)) =   6 : True ; forms of degree d-2 through L: 50
  d=7 s= 2: HF_L(d-2) =  12 = min(s(d-1), C(d+1,3)) =  12 : True ; forms of degree d-2 through L: 44
  d=7 s= 3: HF_L(d-2) =  18 = min(s(d-1), C(d+1,3)) =  18 : True ; forms of degree d-2 through L: 38
  d=7 s= 4: HF_L(d-2) =  24 = min(s(d-1), C(d+1,3)) =  24 : True ; forms of degree d-2 through L: 32
  d=7 s= 5: HF_L(d-2) =  30 = min(s(d-1), C(d+1,3)) =  30 : True ; forms of degree d-2 through L: 26
  d=7 s= 6: HF_L(d-2) =  36 = min(s(d-1), C(d+1,3)) =  36 : True ; forms of degree d-2 through L: 20
  d=7 s= 7: HF_L(d-2) =  42 = min(s(d-1), C(d+1,3)) =  42 : True ; forms of degree d-2 through L: 14
  d=7 s= 8: HF_L(d-2) =  48 = min(s(d-1), C(d+1,3)) =  48 : True ; forms of degree d-2 through L: 8
  d=7 s= 9: HF_L(d-2) =  54 = min(s(d-1), C(d+1,3)) =  54 : True ; forms of degree d-2 through L: 2
  d=7 s=10: HF_L(d-2) =  56 = min(s(d-1), C(d+1,3)) =  56 : True ; forms of degree d-2 through L: 0
  d=7 s=11: HF_L(d-2) =  56 = min(s(d-1), C(d+1,3)) =  56 : True ; forms of degree d-2 through L: 0
  d=7 s=12: HF_L(d-2) =  56 = min(s(d-1), C(d+1,3)) =  56 : True ; forms of degree d-2 through L: 0
  d=7 s=13: HF_L(d-2) =  56 = min(s(d-1), C(d+1,3)) =  56 : True ; forms of degree d-2 through L: 0
  d=7 s=14: HF_L(d-2) =  56 = min(s(d-1), C(d+1,3)) =  56 : True ; forms of degree d-2 through L: 0
  d=7 s=15: HF_L(d-2) =  56 = min(s(d-1), C(d+1,3)) =  56 : True ; forms of degree d-2 through L: 0

general lines: dim (I_L^(2))_d  (forms of degree d singular along all s lines)
  d=5 s=5: dim I^(2)_d = 0  (alpha(I) = 4)
  d=5 s=6: dim I^(2)_d = 0  (alpha(I) = 4)
  d=6 s=7: dim I^(2)_d = 0  (alpha(I) = 5)
  d=6 s=8: dim I^(2)_d = 0  (alpha(I) = 5)
  d=6 s=10: dim I^(2)_d = 0  (alpha(I) = 6)
