The induced norm of the matrix $A$ as a map from $(\mathbb R^n , \| \cdot \|_p)$ to $(\mathbb R^m, \| \cdot \|_q)$ is given by $$ \| A \|_{p,q} = \sup_{x\in\mathbb{R}^n\setminus \{0\}} \frac{\|Ax\|_q}{\|x\|_p}.$$

I would like to compute $\| \cdot \|_{2,\infty}$. In this paper: On the Calculation of the $l_2\to l_1$ Induced Matrix Norm, the authors presented the results for any $p,q\in\{1,2,\infty\}$, except for $p=2$ and $q=\infty$.

So I would like to know if this is still an open problem. And if it is, then is there any result on finding a tight and easy-to-compute upper bound on the norm?

Thank you in advance.