The Komlós Problem in Matrix-Multiplication Time

We give a randomized algorithm that, for an $m\times n$ matrix whose columns have Euclidean norm at most one, finds a signing with discrepancy below $99$ in expected $\widetilde O(L_{\mathrm{in}}+n^ω)$ bit operations, where $L_{\mathrm{in}}$ is the input encoding length and $ω$ is the exponent of ma