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We study the optimal coreset size for Euclidean $(k,z)$-clustering, where $z\ge1$ is fixed. Huang, Li, and Wu (STOC 2024) proved a lower bound of $Ω_z(k\varepsilon^{-z-2})$ for $\varepsilon\gtrsim_z k^{-1/(z+2)}$, matchi...