Line integrals along t-design curves yield exact quadrature rules for polynomials of degree t on the d-sphere, whereas the classical t-designs use point evaluations for quadrature. We will show that on the 2-sphere in R3 t-design curves of the optimal length O(t) exist, and perhaps indicate the existence of t-design curves for higher-dimensional spheres.
https://univienna.zoom.us/j/62077153839?pwd=T3pxeHNRNEU0RlFoY1J2cnIzbzU5dz09