Explicit constructions of higher-strength spherical designs

Construct explicit families of spherical t-designs with few points for every strength t at least 6.

Background

The paper’s upper-bound arguments establish existence through algebraic, probabilistic, and convex-geometric methods, but they do not provide specific point sets in general. The authors distinguish this constructive issue from the cardinality problem and ask for concrete families beyond the small strengths treated explicitly.

The requested constructions should apply to strengths t≥6 and use few points.