A prior work by Song, Ye, Yin and Zhang claiming to improve row count to O(ε^-2 d log^3 n) has a flawed proof that relies on an independence assumption that does not hold in general

A subsequent work of Song, Ye, Yin and Zhang claimed to improve the row count to $O(ε^{-2}d\log^3 n)$. Unfortunately, their proof relies on an independence assumption that does not hold in general, and we exhibit an explicit instance on which it fails.

http://arxiv.org/abs/2608.26552v1