{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:54:34Z","timestamp":1747191274346,"version":"3.40.5"},"reference-count":27,"publisher":"Wiley","license":[{"start":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T00:00:00Z","timestamp":1686009600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computational and Mathematical Methods"],"published-print":{"date-parts":[[2023,6,6]]},"abstract":"<jats:p>We prove the equivalence of two-symbol supersaturated designs (SSDs) with<jats:inline-formula><a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><a:mi>N<\/a:mi><\/a:math><\/jats:inline-formula>(even) rows,<jats:inline-formula><c:math xmlns:c=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><c:mi>m<\/c:mi><\/c:math><\/jats:inline-formula>columns, and<jats:inline-formula><e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><e:msub><e:mrow><e:mi>s<\/e:mi><\/e:mrow><e:mrow><e:mi mathvariant=\"normal\">max<\/e:mi><\/e:mrow><\/e:msub><e:mo>=<\/e:mo><e:mn>4<\/e:mn><e:mi>t<\/e:mi><e:mo>+<\/e:mo><e:mi>i<\/e:mi><\/e:math><\/jats:inline-formula>, where<jats:inline-formula><h:math xmlns:h=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M5\"><h:mi>i<\/h:mi><h:mo>\u2208<\/h:mo><h:mfenced open=\"{\" close=\"}\"><h:mrow><h:mn>0<\/h:mn><h:mo>,<\/h:mo><h:mn>2<\/h:mn><\/h:mrow><\/h:mfenced><\/h:math><\/jats:inline-formula>and<jats:inline-formula><l:math xmlns:l=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M6\"><l:mi>t<\/l:mi><l:mo>\u2208<\/l:mo><l:msup><l:mrow><l:mi>\u2124<\/l:mi><\/l:mrow><l:mrow><l:mo>\u2265<\/l:mo><l:mn>0<\/l:mn><\/l:mrow><\/l:msup><\/l:math><\/jats:inline-formula>and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most<jats:inline-formula><n:math xmlns:n=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M7\"><n:mfenced open=\"(\" close=\")\"><n:mrow><n:mi>N<\/n:mi><n:mo>+<\/n:mo><n:mn>4<\/n:mn><n:mi>t<\/n:mi><n:mo>+<\/n:mo><n:mi>i<\/n:mi><\/n:mrow><\/n:mfenced><n:mo>\/<\/n:mo><n:mn>4<\/n:mn><\/n:math><\/jats:inline-formula>points. Using this equivalence, we formulate the search for two-symbol<jats:inline-formula><r:math xmlns:r=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M8\"><r:mi>E<\/r:mi><r:mfenced open=\"(\" close=\")\"><r:mrow><r:msup><r:mrow><r:mi>s<\/r:mi><\/r:mrow><r:mrow><r:mn>2<\/r:mn><\/r:mrow><\/r:msup><\/r:mrow><\/r:mfenced><\/r:math><\/jats:inline-formula>-optimal and minimax-optimal SSDs with<jats:inline-formula><v:math xmlns:v=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M9\"><v:msub><v:mrow><v:mi>s<\/v:mi><\/v:mrow><v:mrow><v:mi mathvariant=\"normal\">max<\/v:mi><\/v:mrow><\/v:msub><v:mo>\u2208<\/v:mo><v:mfenced open=\"{\" close=\"}\"><v:mrow><v:mn>2<\/v:mn><v:mo>,<\/v:mo><v:mn>4<\/v:mn><v:mo>,<\/v:mo><v:mn>6<\/v:mn><\/v:mrow><\/v:mfenced><\/v:math><\/jats:inline-formula>as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found<jats:inline-formula><ab:math xmlns:ab=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M10\"><ab:mi>E<\/ab:mi><ab:mfenced open=\"(\" close=\")\"><ab:mrow><ab:msup><ab:mrow><ab:mi>s<\/ab:mi><\/ab:mrow><ab:mrow><ab:mn>2<\/ab:mn><\/ab:mrow><\/ab:msup><\/ab:mrow><\/ab:mfenced><\/ab:math><\/jats:inline-formula>-optimal and minimax-optimal SSDs achieving the sharpest known<jats:inline-formula><eb:math xmlns:eb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M11\"><eb:mi>E<\/eb:mi><eb:mfenced open=\"(\" close=\")\"><eb:mrow><eb:msup><eb:mrow><eb:mi>s<\/eb:mi><\/eb:mrow><eb:mrow><eb:mn>2<\/eb:mn><\/eb:mrow><\/eb:msup><\/eb:mrow><\/eb:mfenced><\/eb:math><\/jats:inline-formula>lower bound with<jats:inline-formula><ib:math xmlns:ib=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M12\"><ib:msub><ib:mrow><ib:mi>s<\/ib:mi><\/ib:mrow><ib:mrow><ib:mi mathvariant=\"normal\">max<\/ib:mi><\/ib:mrow><\/ib:msub><ib:mo>\u2208<\/ib:mo><ib:mfenced open=\"{\" close=\"}\"><ib:mrow><ib:mn>2<\/ib:mn><ib:mo>,<\/ib:mo><ib:mn>4<\/ib:mn><ib:mo>,<\/ib:mo><ib:mn>6<\/ib:mn><\/ib:mrow><\/ib:mfenced><\/ib:math><\/jats:inline-formula>of sizes<jats:inline-formula><nb:math xmlns:nb=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M13\"><nb:mfenced open=\"(\" close=\")\"><nb:mrow><nb:mi>N<\/nb:mi><nb:mo>,<\/nb:mo><nb:mi>m<\/nb:mi><\/nb:mrow><\/nb:mfenced><nb:mo>=<\/nb:mo><nb:mfenced open=\"(\" close=\")\"><nb:mrow><nb:mn>16<\/nb:mn><nb:mo>,<\/nb:mo><nb:mn>25<\/nb:mn><\/nb:mrow><\/nb:mfenced><\/nb:math><\/jats:inline-formula>, (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.<\/jats:p>","DOI":"10.1155\/2023\/9431476","type":"journal-article","created":{"date-parts":[[2023,6,6]],"date-time":"2023-06-06T21:51:24Z","timestamp":1686088284000},"page":"1-24","source":"Crossref","is-referenced-by-count":2,"title":["A Bit-Parallel Tabu Search Algorithm for Finding<a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><a:mi>E<\/a:mi><a:mfenced open=\"(\" close=\")\"><a:mrow><a:msup><a:mrow><a:mi>s<\/a:mi><\/a:mrow><a:mrow><a:mn>2<\/a:mn><\/a:mrow><\/a:msup><\/a:mrow><\/a:mfenced><\/a:math>-Optimal and Minimax-Optimal Supersaturated Designs"],"prefix":"10.1155","volume":"2023","author":[{"given":"Luis B.","family":"Morales","sequence":"first","affiliation":[{"name":"Unidad Acad, IIMAS Estado de Yucat\u00e1n, Universidad Nacional Aut\u00f3noma de M\u00e9xico, M\u00e9rida, Yuc, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7117-3502","authenticated-orcid":true,"given":"Dursun A.","family":"Bulutoglu","sequence":"additional","affiliation":[{"name":"Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1962.10490035"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2006.07.008"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1080\/00401706.1996.10484417"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2005.03.007"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2007.05.044"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1080\/15598608.2011.10412034"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2011.12.021"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1002\/jcd.21341"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jspi.2012.09.014"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1.3.190"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1016\/j.cor.2010.07.019"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1002\/jcd.21658"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1198\/004017007000000452"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1080\/08982110601057146"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1093\/biomet\/80.3.661"},{"key":"16","first-page":"272","article-title":"Applying supersaturated experimental designs to the study of composite sampling for monitoring pesticide residues in water","volume":"22","author":"R. 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