Bounds for approximate L2 spherical designs

Improve the known upper or lower bounds for the minimum size of approximate L^2 spherical designs.

Background

The paper introduces L2-approximate spherical designs and proves separate lower and upper bounds on their size. It observes that these bounds are not as tight as the corresponding bounds obtained for approximate tensor designs.

The unresolved problem is to improve at least one side of the size estimates for approximate L2-designs.

References

Improve the upper or lower bound for approximate $L2$-designs.

— Fixed-strength spherical designs  (2502.06002 - Dillon, 9 Feb 2025) in Section 6, Open questions, Problem following the discussion of approximate designs