We prove the equivalence of two-symbol supersaturated designs (SSDs) with $N$ (even) rows, $m$ columns, $s_{\rm max} = 4t +i$, where $i\in\{0,2\}$, $t \in \mathbb{Z}^{\geq 0}$ and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most $(N+4t+i)/4$ points. Using this equivalence, we formulate the search for two-symbol E($s^2$)-optimal and minimax-optimal SSDs with $s_{\max} \in \{2,4,6\}$ as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found E($s^2$)-optimal and minimax-optimal SSDs achieving the sharpest known E($s^2$) lower bound with $s_{\max} \in \{2,4,6\}$ of sizes $(N,m)=(16,25), (16,26), (16,27), (18,23),(18,24),(18,25),(18,26),(18,27),(18, 28),$ $(18,29),(20,21),(22,22),(22,23),(24,24)$, and $(24,25)$. In each of these cases no such SSD could previously be found.

翻译：我们证明了具有$N$（偶数）行、$m$列、$s_{\rm max} = 4t +i$（其中$i\in\{0,2\}$，$t \in \mathbb{Z}^{\geq 0}$）的双符号超饱和设计与任意两个区组交集点数不超过$(N+4t+i)/4$的可分解不完全区组设计等价。利用这一等价关系，我们将$s_{\max} \in \{2,4,6\}$情形下双符号E($s^2$)-最优和极小化极大最优SSD的搜索问题转化为寻找区组交集满足相应条件的RIBD问题。由此可开发一种一位并行禁忌搜索算法。该TS算法找到了$s_{\max} \in \{2,4,6\}$时达到已知最紧E($s^2$)下界的E($s^2$)-最优和极小化极大最优SSD，其规模$(N,m)$分别为$(16,25), (16,26), (16,27), (18,23),(18,24),(18,25),(18,26),(18,27),(18, 28),$$(18,29),(20,21),(22,22),(22,23),(24,24)$和$(24,25)$。在以上每种情形中，此前均未能找到此类SSD。