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相交点数不超过$(N+4t+i)/4$的可分解不完全区组设计之间的等价性。利用这一等价性，我们将$s_{\max}\in\{2,4,6\}$的双符号E($s^2$)-最优和极小极大最优超饱和设计的搜索问题转化为寻找相应相交条件的可分解不完全区组设计问题。由此开发了一种比特并行禁忌搜索算法。该算法找到了针对$s_{\max}\in\{2,4,6\}$且尺寸为$(N,m)=(16,25),(16,26),(16,27),(18,23),(18,24),(18,25),(18,26),(18,27),(18,28),(18,29),(20,21),(22,22),(22,23),(24,24),(24,25)$的E($s^2$)-最优和极小极大最优超饱和设计，这些设计达到了已知最紧的E($s^2$)下界。在所有这些情形下，此前均未能找到此类超饱和设计。