Numerical computation of triangular complex spherical designs with small mesh ratio

This paper provides triangular spherical designs for the complex unit sphere Ω^d⊂ℂ^d by exploiting the natural correspondence with the real unit sphere S^2d−1⊂R^2d. A variational characterization of triangular complex designs is provided, with particular emphasis on numerical computation of efficient triangular complex designs with good geometric properties as measured by their mesh ratio. We give numerical examples of triangular spherical t-designs on complex unit spheres of dimension d=2 to 6.