For k = 4

These added points are

x_i = (x_i1 , x_i2 , x_i3 , x_i4), i = 1, …, 7,

where x_i1 = 2sinθ_i3sinθ_i2cosθ_i1, x_i2 = 2sinθ_i3sinθ_i2sinθ_i1, x_i3 = 2sinθ_i3cosθ_i2, and x_i4 = 2cosθ_i3.

After 400 iterations, the optimal added points obtained by BA sampler are

.

The maximum of P_eff value is 0.7115.

For k = 4, the determinants of X^’X for 400 × 10 × 21 = 84000 steps.