add result of S^5

n_sphere/slides.html

@@ -515,6 +515,14 @@
 
 ---
 
+## Result for $S^5$
+
+![Result for $S^5$. Compared with cylindrical mapping method.](res-S5-cylin.svg)
+
+: Result for $S^5$. Compared with cylindrical mapping method.
+
+---
+
 ## Conclusions
 
 This note provides a comprehensive discussion of low discrepancy sampling methods for n-dimensional spheres. It introduces a proposed methodology for generating low-discrepancy sequences on n-dimensional spheres based on the van der Corput sequence, addressing challenges associated with high-dimensional sampling while maintaining desirable properties. This note outlines key concepts such as the van der Corput sequence, Halton sequence, and their applications to unit circles, unit spheres, and higher-dimensional spaces. The document provides detailed explanations and implementations of algorithms for generating points on various dimensional spheres, including the use of Hopf fibration for four-dimensional spheres.