Dimension-Free Dot Product NMSE Under Log-Uniform Quantization

For Z = Σ wᵢxᵢ with independent iid pairs and centroid-condition quantizers, NMSE_Z ≈ NMSE_w + NMSE_x + O(1/N⁴). The NMSE does not grow with dimension d, meaning quantization error in large matrix multiplications is controlled.