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Codes Cryptogr."],"published-print":{"date-parts":[[2023,7]]},"abstract":"Abstract<\/jats:title>The paper deals with t<\/jats:italic>-designs that can be partitioned into s<\/jats:italic>-designs, each missing a point of the underlying set, called point-missing s<\/jats:italic>-resolvable t<\/jats:italic>-designs, with emphasis on their applications in constructing t<\/jats:italic>-designs. The problem considered may be viewed as a generalization of overlarge sets which are defined as a partition of all the $$\\left( {\\begin{array}{c}v +1\\\\ k\\end{array}}\\right) $$<\/jats:tex-math>\n \n \n \n \n \n \n v<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n \n \n \n \n k<\/mml:mi>\n <\/mml:mrow>\n <\/mml:mtd>\n <\/mml:mtr>\n <\/mml:mtable>\n <\/mml:mrow>\n <\/mml:mfenced>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>k<\/jats:italic>-sets chosen from a $$(v+1)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n v<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-set X<\/jats:italic> into $$(v+1)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n v<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> mutually disjoint s<\/jats:italic>-$$(v,k,\\delta )$$<\/jats:tex-math>\n \n (<\/mml:mo>\n v<\/mml:mi>\n ,<\/mml:mo>\n k<\/mml:mi>\n ,<\/mml:mo>\n \u03b4<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> designs, each missing a different point of X<\/jats:italic>. Among others, it is shown that the existence of a point-missing $$(t-1)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n t<\/mml:mi>\n -<\/mml:mo>\n 1<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>-resolvable t<\/jats:italic>-$$(v,k,\\lambda )$$<\/jats:tex-math>\n \n (<\/mml:mo>\n v<\/mml:mi>\n ,<\/mml:mo>\n k<\/mml:mi>\n ,<\/mml:mo>\n \u03bb<\/mml:mi>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> design leads to the existence of a t<\/jats:italic>-$$(v,k+1,\\lambda ')$$<\/jats:tex-math>\n \n (<\/mml:mo>\n v<\/mml:mi>\n ,<\/mml:mo>\n k<\/mml:mi>\n +<\/mml:mo>\n 1<\/mml:mn>\n ,<\/mml:mo>\n \n \u03bb<\/mml:mi>\n \u2032<\/mml:mo>\n <\/mml:msup>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> design. As a result, we derive various infinite series of 4-designs with constant index using overlarge sets of disjoint Steiner quadruple systems. These have parameters 4-$$(3^n,5,5)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n \n 3<\/mml:mn>\n n<\/mml:mi>\n <\/mml:msup>\n ,<\/mml:mo>\n 5<\/mml:mn>\n ,<\/mml:mo>\n 5<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, 4-$$(3^n+2,5,5)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n \n 3<\/mml:mn>\n n<\/mml:mi>\n <\/mml:msup>\n +<\/mml:mo>\n 2<\/mml:mn>\n ,<\/mml:mo>\n 5<\/mml:mn>\n ,<\/mml:mo>\n 5<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and 4-$$(2^n+1,5,5)$$<\/jats:tex-math>\n \n (<\/mml:mo>\n \n 2<\/mml:mn>\n n<\/mml:mi>\n <\/mml:msup>\n +<\/mml:mo>\n 1<\/mml:mn>\n ,<\/mml:mo>\n 5<\/mml:mn>\n ,<\/mml:mo>\n 5<\/mml:mn>\n )<\/mml:mo>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, for $$n \\ge 2$$<\/jats:tex-math>\n \n n<\/mml:mi>\n \u2265<\/mml:mo>\n 2<\/mml:mn>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, and were unknown until now. We also include a recursive construction of point-missing s<\/jats:italic>-resolvable t<\/jats:italic>-designs and its application.<\/jats:p>","DOI":"10.1007\/s10623-023-01206-8","type":"journal-article","created":{"date-parts":[[2023,4,3]],"date-time":"2023-04-03T15:43:08Z","timestamp":1680536588000},"page":"2497-2508","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Point-missing s-resolvable t-designs: infinite series of 4-designs with constant index"],"prefix":"10.1007","volume":"91","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7453-357X","authenticated-orcid":false,"given":"Tran van","family":"Trung","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2023,3,30]]},"reference":[{"key":"1206_CR1","doi-asserted-by":"publisher","first-page":"320","DOI":"10.1016\/S0021-9800(69)80096-7","volume":"6","author":"WO Alltop","year":"1969","unstructured":"Alltop W.O.: An infinite class of 4-designs. 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