On the linear and hereditary discrepancies (Q1568788)

Let \(A\) be an \(m\times n\) 0-1-matrix (incidence matrix of a set system) and let \[ \begin{aligned} \text{disc } (A)&=\min_{x\in \{-1, 1\}^n} \|Ax \|_\infty\\ \text{herdisc } (A)&=\max_{B \text{ submatrix of } A} \text{disc }(B)\\ \text{lindisc}_1 (A)&=\max_{w\in\{-1, 0, 1\}^n} \min_{x\in\{-1, 1\}^n} \|A(x-w)\|_\infty \end{aligned} \] The author proves that there is some 0-1-matrix \(A_0\) such that \(\text{lindisc}_1(A)\geq 2\) for any 0-1-matrix \(A\) containing \(A_0\) as a submatrix.