Linear-algebraic lower bounds for approximate designs

Establish a purely linear-algebraic lower-bound proof for approximate spherical designs that is comparable to the paper's lower bound for approximate L^2 spherical 2t-designs.

Background

The paper proves a lower bound for approximate designs using the Delsarte-style linear programming method and Gegenbauer polynomials. In contrast, it gives a short linear-algebraic proof for the corresponding lower bound for exact designs.

The open question asks whether an analogous concise argument based solely on linear algebra can recover a lower bound of comparable strength for approximate designs.