10.1155/2023/9431476">
 

Document Type

Article

Publication Date

6-6-2023

Abstract

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.

Comments

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

This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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

Source Publication

Computational and Mathematical Methods

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