Exact covering radii of higher-dimensional balls

Determine the exact values of the covering radii cov_{B^n}(m) for higher-dimensional Euclidean unit balls, particularly for n≥3 and the values of m for which these quantities are currently unknown.

Background

The covering-radius estimate d_GH(Bm,Bn)≥1−cov_{Bn}(m) is one of the paper’s principal dimension-dependent bounds. Applying it quantitatively requires optimal finite m-point coverings of Bn. The paper states that these optimal covering radii are not known for most m in dimensions n≥3, so determining them remains an unresolved geometric optimization problem.

References

For higher values of $n$ ($n\geq 3$), the exact values of $cov_{Bn}(m)$ remain unknown for most $m$, necessitating the use of upper and lower bounds for $cov_{Bn}(m)$.

— Gromov--Hausdorff Distance Between Euclidean Unit Balls  (2609.09652 - Adams et al., 9 Sep 2026) in Section 4, paragraph following the comparison of Theorem 2.2 and Proposition 4.1