{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:23:12Z","timestamp":1740122592443,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T00:00:00Z","timestamp":1653350400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T00:00:00Z","timestamp":1653350400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100008349","name":"Universit\u00e4t Duisburg-Essen","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100008349","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2022,7]]},"abstract":"Abstract<\/jats:title>The paper introduces a method for constructing 2-resolvable t<\/jats:italic>-designs for $$t=3,4$$<\/jats:tex-math>\n \n t<\/mml:mi>\n =<\/mml:mo>\n 3<\/mml:mn>\n ,<\/mml:mo>\n 4<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>. The main idea is based on the assumption that there exists a partition of a t<\/jats:italic>-design into Steiner 2-designs. A remarkable property of the method is that it enables the construction of 2-resolvable t<\/jats:italic>-designs with a large variety of block sizes. For $$t=4$$<\/jats:tex-math>\n \n t<\/mml:mi>\n =<\/mml:mo>\n 4<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, it is required that the Steiner 2-designs of the partition are projective planes and this case would also lead to a construction of 3-resolvable 5-designs. For instance, we show the existence of an infinite series of 3-resolvable 5-designs having $$N=5$$<\/jats:tex-math>\n \n N<\/mml:mi>\n =<\/mml:mo>\n 5<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> resolution classes with parameters 5-$$(14+8m,7, 10(9+8m)(1+m))$$<\/jats:tex-math>\n \n (<\/mml:mo>\n 14<\/mml:mn>\n +<\/mml:mo>\n 8<\/mml:mn>\n m<\/mml:mi>\n ,<\/mml:mo>\n 7<\/mml:mn>\n ,<\/mml:mo>\n 10<\/mml:mn>\n (<\/mml:mo>\n 9<\/mml:mn>\n +<\/mml:mo>\n 8<\/mml:mn>\n m<\/mml:mi>\n )<\/mml:mo>\n (<\/mml:mo>\n 1<\/mml:mn>\n +<\/mml:mo>\n m<\/mml:mi>\n )<\/mml:mo>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> for any $$m \\ge 0$$<\/jats:tex-math>\n \n m<\/mml:mi>\n \u2265<\/mml:mo>\n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> as a byproduct. Moreover, it turns out that the method is very effective, as it yields infinitely many 2-resolvable 3-designs. However, the question of simplicity of the constructed designs has not been yet investigated.<\/jats:p>","DOI":"10.1007\/s10623-022-01056-w","type":"journal-article","created":{"date-parts":[[2022,5,25]],"date-time":"2022-05-25T05:10:20Z","timestamp":1653455420000},"page":"1567-1583","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A method of constructing 2-resolvable t-designs for $$t=3,4$$"],"prefix":"10.1007","volume":"90","author":[{"given":"Tran","family":"van Trung","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,5,24]]},"reference":[{"key":"1056_CR1","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1006\/jcta.1996.0093","volume":"76","author":"S Ajoodani-Namini","year":"1996","unstructured":"Ajoodani-Namini S.: Extending large sets of $$t$$-designs. J. Comb. Theory A 76, 139\u2013144 (1996).","journal-title":"J. Comb. 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