Beck–Fiala discrepancy conjecture

Let $\mathcal H$ be a hypergraph on a finite ground set $X$, where every vertex has degree at most $d$. Beck–Fiala's conjecture. There exists a function $f:X\rightarrow\{-1,1\}$ such that for every $e\in\mathcal H$,

$$\left|\sum_{x\in e}f(x)\right|\leqslant C\sqrt d,$$

where $C>0$ is an absolute constant. The source describes this as the hypergraph-colouring companion to Komlós's conjecture and notes that Komlós's conjecture implies it; it is presented as open.