{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:59:58Z","timestamp":1776844798969,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"255","license":[{"start":{"date-parts":[[2007,3,13]],"date-time":"2007-03-13T00:00:00Z","timestamp":1173744000000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    A major search program is described that has been used to determine a set of five-dimensional\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper K\">\n                        <mml:semantics>\n                          <mml:mi>K<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">K<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -optimal lattice rules of enhanced trigonometric degrees up to 12. The program involved a distributed search, in which approximately 190 CPU-years were shared between more than 1,400 computers in many parts of the world.\n                  <\/p>","DOI":"10.1090\/s0025-5718-06-01845-x","type":"journal-article","created":{"date-parts":[[2006,5,24]],"date-time":"2006-05-24T14:43:01Z","timestamp":1148481781000},"page":"1467-1480","source":"Crossref","is-referenced-by-count":7,"title":["Five-dimensional \ud835\udc3e-optimal lattice rules"],"prefix":"10.1090","volume":"75","author":[{"given":"J.","family":"Lyness","sequence":"first","affiliation":[]},{"given":"Tor","family":"S\u00f8revik","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2006,3,13]]},"reference":[{"issue":"6","key":"1","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1016\/j.jco.2003.08.001","article-title":"Five- and six-dimensional lattice rules generated by structured matrices","volume":"19","author":"Cools, Ronald","year":"2003","journal-title":"J. Complexity","ISSN":"https:\/\/id.crossref.org\/issn\/0885-064X","issn-type":"print"},{"issue":"236","key":"2","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1090\/S0025-5718-01-01326-6","article-title":"Three- and four-dimensional \ud835\udc3e-optimal lattice rules of moderate trigonometric degree","volume":"70","author":"Cools, Ronald","year":"2001","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"216","key":"3","doi-asserted-by":"publisher","first-page":"1583","DOI":"10.1090\/S0025-5718-96-00767-3","article-title":"Minimal cubature formulae of trigonometric degree","volume":"65","author":"Cools, Ronald","year":"1996","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"3","key":"4","doi-asserted-by":"publisher","first-page":"405","DOI":"10.1093\/imanum\/9.3.405","article-title":"An introduction to lattice rules and their generator matrices","volume":"9","author":"Lyness, J. N.","year":"1989","journal-title":"IMA J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0272-4979","issn-type":"print"},{"issue":"3","key":"5","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1016\/S0885-064X(03)00005-0","article-title":"Notes on lattice rules","volume":"19","author":"Lyness, J. N.","year":"2003","journal-title":"J. Complexity","ISSN":"https:\/\/id.crossref.org\/issn\/0885-064X","issn-type":"print"},{"key":"6","unstructured":"[LyCo00] J. N. Lyness and R. Cools, Notes on a search for optimal lattice rules, in Cubature Formulae and Their Applications (M. V. Noskov, ed.), 259\u2013273, Krasnoyarsk STU, 2000. Also available as Argonne National Laboratory Preprint ANL\/MCS-P829-0600."},{"issue":"2","key":"7","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/BF02253429","article-title":"A search program for finding optimal integration lattices","volume":"47","author":"Lyness, J. N.","year":"1991","journal-title":"Computing","ISSN":"https:\/\/id.crossref.org\/issn\/0010-485X","issn-type":"print"},{"issue":"4","key":"8","doi-asserted-by":"publisher","first-page":"665","DOI":"10.1007\/BF01994849","article-title":"An algorithm for finding optimal integration lattices of composite order","volume":"32","author":"Lyness, J. N.","year":"1992","journal-title":"BIT","ISSN":"https:\/\/id.crossref.org\/issn\/0006-3835","issn-type":"print"},{"issue":"204","key":"9","doi-asserted-by":"publisher","first-page":"799","DOI":"10.2307\/2153254","article-title":"Lattice rules by component scaling","volume":"61","author":"Lyness, J. N.","year":"1993","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"issue":"245","key":"10","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1090\/S0025-5718-03-01534-5","article-title":"Four-dimensional lattice rules generated by skew-circulant matrices","volume":"73","author":"Lyness, J. N.","year":"2004","journal-title":"Math. Comp.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5718","issn-type":"print"},{"key":"11","unstructured":"[Min11] H. Minkowski, Gesammelte Abhandlungen, reprint (originally published in 2 volumes, Leipzig, 1911), Chelsea Publishing Company, 1967."},{"key":"12","isbn-type":"print","first-page":"221","article-title":"Lower bounds for the number of nodes in cubature formulae","author":"M\u00f6ller, H. M.","year":"1979","ISBN":"https:\/\/id.crossref.org\/isbn\/3764310146"},{"issue":"15","key":"13","first-page":"7","article-title":"Cubature formulas that are exact for trigonometric polynomials","author":"Mysovskikh, I. P.","year":"1988","journal-title":"Metody Vychisl.","ISSN":"https:\/\/id.crossref.org\/issn\/0131-2146","issn-type":"print"},{"issue":"9","key":"14","first-page":"1414","article-title":"Cubature formulas for functions that are periodic with respect to some of the variables","volume":"31","author":"Noskov, M. V.","year":"1991","journal-title":"Zh. Vychisl. Mat. i Mat. Fiz.","ISSN":"https:\/\/id.crossref.org\/issn\/0044-4669","issn-type":"print"},{"key":"15","doi-asserted-by":"crossref","unstructured":"[SoMy01] T. S\u00f8revik and J. F. Myklebust, GRISK: An Internet based search for K-optimal lattice rules, in Proceedings of PARA2000, Lecture Notes in Computer Science 1947, 196\u2013205, Springer Verlag, 2001.","DOI":"10.1007\/3-540-70734-4_24"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2006-75-255\/S0025-5718-06-01845-X\/S0025-5718-06-01845-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-255\/S0025-5718-06-01845-X\/S0025-5718-06-01845-X.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T14:36:42Z","timestamp":1776782202000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2006-75-255\/S0025-5718-06-01845-X\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3,13]]},"references-count":15,"journal-issue":{"issue":"255","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["S0025-5718-06-01845-X"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-06-01845-x","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2006,3,13]]}}}