For k = 3

The polar coordinates of the two support points are

(x₁₁ , x₁₂ , x₁₃) = (sinθ₁₂ cosθ₁₁ , sinθ₁₂ sinθ₁₁ , cosθ₁₂),

and

(x₂₁ , x₂₂ , x₂₃) = (sinθ₂₂ cosθ₂₁ , sinθ₂₂ sinθ₂₁ , cosθ₂₂),

where .

Following the same approach for the case of two factors, two optimal added points are to choose two perpendicular points from six star points. For example: () and (). At this time, the corresponding P_eff is 0.6048.

Best Angle sampler

Example:

We suppose that T(t) = (5t)^-2/3 and N_t = 10. After 400 iterations of BA sampler, the best added support points are

These two added points for the D-optimal minimal-point designs are any two perpendicular points of six star points.