The maximum number of columns in E ( s 2 ) $\,E({s}^{2})$ -optimal supersaturated designs with 16 rows and s max = 4 ${s}_{{\rm{\max }}}=4$ is 60

We show that the maximum number of columns in $E\left(s^2\right)$-optimal supersaturated designs (SSDs) with 16 rows and $s_{\max }=4$ is 60 by showing that there exists no resolvable 2-(16, 8, 35) design such that any two blocks from different parallel classes intersect in 3, 5, or 4 points. This is accomplished by an exhaustive computer search that uses the parallel class intersection pattern method to reduce the search space. We also classify all nonisomorphic $E\left(s^2\right)$-optimal 5-circulant SSDs with 16 rows and $s_{\max }=8$.