For k = 8

These added support points are

x_i = (x_i1 , x_i2 , x_i3 , x_i4 , x_i5 , x_i6, x_i7, x_i8), i = 1, …, 15,

where x_i1 =sinθ_i7sinθ_i6sin θ_i5sinθ_i4sinθ_i3sinθ_i2cosθ_i1, x_i2 =sinθ_i7sinθ_i6sinθ_i5sin θ_i4sinθ_i3sinθ_i2sin θ_i1, x_i3 =sinθ_i7sinθ_i6sinθ_i5sin θ_i4sinθ_i3cosθ_i2, x_i4 =sinθ_i7sinθ_i6sinθ_i5sin θ_i4cosθ_i3, x_i5 =sinθ_i7sinθ_i6sinθ_i5cosθ_i4, x_i6 =sinθ_i7sinθ_i6cosθ_i5, x_i7 =sinθ_i7cosθ_i6, and x_i8 =cosθ_i7.

After 600 iterations, the optimal added points obtained by BA sampler are

.

The maximum of P_eff value is 0.6278.

For k = 8, the determinants of X^’X for 600 × 10 × 105 = 630000 steps.