n = 1, p = 0 (no noise)

with result qubit initialized to H|1> = |->
i.e. using membership oracle cf. Cleve, et. al.
probability of correct measurement = 1

  % ./BV -dd 1 0 1 1
   BV: qn = 1, N = 2, p = 0, a = 1, b = 1, m = 3
    q: (0,0) (1,0) (0,0) (0,0)
   Hr: (0.707107,0) (-0.707107,0) (0,0) (0,0)
   Hc: (0.5,0) (-0.5,0) (0.5,0) (-0.5,0)
    f: (-0.5,0) (0.5,0) (0.5,0) (-0.5,0)
    H: (0,0) (-0.707107,0) (0,0) (0.707107,0)
    H: (0,0) (0,0) (0,0) (-1,0)
    q: (0,0) (0,0) (0,0) (-1,0)
   BV: q[3] = (-1,0), abs2 = 1

with result qubit initialized to |0>
i.e. using example oracle cf. Cross, et. al.
probability of correct measurement = 0.5

  % ./BV -dd0 1 0 1 1
   BV: qn = 1, N = 2, p = 0, a = 1, b = 1, m = 3
    q: (1,0) (0,0) (0,0) (0,0)
   Hc: (0.707107,0) (0,0) (0.707107,0) (0,0)
    f: (0,0) (0.707107,0) (0.707107,0) (0,0)
    H: (0.5,0) (-0.5,0) (0.5,0) (0.5,0)
    H: (0.707107,0) (0,0) (0,0) (-0.707107,0)
    q: (0.707107,0) (0,0) (0,0) (-0.707107,0)
   BV: q[3] = (-0.707107,0), abs2 = 0.5

---

n = 2, p = 0 (no noise)

% ./BV -d 2 0 2 1
 BV: qn = 2, N = 4, p = 0, a = 2, b = 1, m = 5
  q: (0,0) (0,0) (0,0) (0,0) (0,0) (-1,0) (0,0) (0,0)
 BV: q[5] = (-1,0), abs2 = 1

% ./BV -d0 2 0 2 1
 BV: qn = 2, N = 4, p = 0, a = 2, b = 1, m = 5
  q: (0.707107,0) (0,0) (0,0) (0,0) (0,0) (-0.707107,0) (0,0) (0,0)
 BV: q[5] = (-0.707107,0), abs2 = 0.5

---

n = 2, p = 0.5 (noise)

% ./BV -d 2 0.5 2 1
 BV: qn = 2, N = 4, p = 0.5, a = 2, b = 1, m = 5
  q: (0.25,0) (0.25,0) (0.25,0) (0.25,0) (0.25,0) (4.59227e-17,0.75) (0.25,0) (0.25,0)
 BV: q[5] = (4.59227e-17,0.75), abs2 = 0.5625

% ./BV -d0 2 0.5 2 1
 BV: qn = 2, N = 4, p = 0.5, a = 2, b = 1, m = 5
  q: (0.559017,0) (0.25,0) (0.25,0) (0.25,0) (0.25,0) (3.42288e-17,0.559017) (0.25,0) (0.25,0)
 BV: q[5] = (3.42288e-17,0.559017), abs2 = 0.3125


 P(0) = P(m) = (1-p)*0.5 + p/2**n, all other P(i) = p/2**n, with n = qn+1 = 3 here