Smallest unweighted approximate spherical designs

Determine the minimum size of unweighted L^2-approximate and tensor-approximate t-designs in R^d.

Background

The upper-bound constructions for both approximation notions in the paper use weights. Consequently, they do not determine the optimal size of unweighted approximate designs.

The paper asks for the size of the smallest unweighted designs under both the L2 approximation notion and the tensor approximation notion, as a function of d, t, and the approximation parameter.

References

What is the size of the smallest unweighted $L2$- or tensor-approximate $t$-designs in $\Rd$?

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