The K51ml\f3s discrepancy conjecture

For a square matrix $A$, define its discrepancy by

$$\operatorname{disc}(A)=\inf_{x\in\\{\pm1\\}^n}\\|Ax\\|_\infty.$$

K51ml\f3s conjecture. There exists a universal constant $K$ such that every square matrix $A$ whose columns have unit $\ell_2$ norm satisfies

$$\operatorname{disc}(A)\leq K.$$

This conjecture is a vector-balancing strengthening of discrepancy bounds for $\pm1$ matrices. It remains open; the best cited lower bound on the possible value of $K$ is $1+\sqrt2$.