Figure 6

Probability density functions of differences of orthogonality defects (in logarithm). This figure is to compare PLLL with the other four basis reduction methods. panel A, $(log{\mathcal{O}}^{\text{PLLL}}-log{\mathcal{O}}^{\text{LLL}})$ for PLLL relative to LLL; panel B, $(log{\mathcal{O}}^{\text{PLLL}}-log{\mathcal{O}}^{\text{DEEP}})$ for PLLL relative to DEEP; panel C, $(log{\mathcal{O}}^{\text{PLLL}}-log{\mathcal{O}}^{\text{SLLL}})$ for PLLL relative to SLLL; and panel D, $(log{\mathcal{O}}^{\text{PLLL}}-log{\mathcal{O}}^{\text{VLLL}})$ for PLLL relative to VLLL. Negative difference values mean better results for PLLL.