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We prove the equivalence of two-symbol supersaturated designs (SSDs) with N (even) rows, m columns, smax=4t+i, where i ∈ {0,2}, t ∈ Z≥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(s2)-optimal and minimax-optimal SSDs with smax ∈ {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(s2)-optimal and minimax-optimal SSDs achieving the sharpest known E(s2) lower bound with smax ∈ {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.


Copyright © 2023 Luis B. Morales and Dursun A. Bulutoglu.

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The manuscript for this article appears in the arXiv e-print repository. arXiv:2303.09104

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Computational and Mathematical Methods