{"id":"https://openalex.org/W2094952117","doi":"https://doi.org/10.1090/s0025-5718-08-02009-7","title":"The construction of good extensible rank-1 lattices","display_name":"The construction of good extensible rank-1 lattices","publication_year":2008,"publication_date":"2008-05-01","ids":{"openalex":"https://openalex.org/W2094952117","doi":"https://doi.org/10.1090/s0025-5718-08-02009-7","mag":"2094952117"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-08-02009-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02009-7","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02009-7/S0025-5718-08-02009-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02009-7/S0025-5718-08-02009-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004856556","display_name":"Josef Dick","orcid":"https://orcid.org/0000-0003-0142-6022"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Josef Dick","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia","School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052381247","display_name":"Friedrich Pillichshammer","orcid":"https://orcid.org/0000-0001-6952-9218"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Friedrich Pillichshammer","raw_affiliation_strings":["Institut f\u00c3\u00bcr Finanzmathematik, Universit\u00c3\u00a4t Linz, Altenbergstra\u00c3\u009fe 69, A-4040 Linz, Austria","Institut f\u00fcr Finanzmathematik Universit\u00e4t Linz Altenbergstra\u00dfe 69 A-4040 Linz, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00c3\u00bcr Finanzmathematik, Universit\u00c3\u00a4t Linz, Altenbergstra\u00c3\u009fe 69, A-4040 Linz, Austria","institution_ids":[]},{"raw_affiliation_string":"Institut f\u00fcr Finanzmathematik Universit\u00e4t Linz Altenbergstra\u00dfe 69 A-4040 Linz, Austria","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111699236","display_name":"Benjamin J. Waterhouse","orcid":null},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Benjamin Waterhouse","raw_affiliation_strings":["School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia","School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney 2052, Australia","institution_ids":["https://openalex.org/I31746571"]},{"raw_affiliation_string":"School of Mathematics and Statistics, University of New South Wales, Sydney, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.7686,"has_fulltext":true,"cited_by_count":52,"citation_normalized_percentile":{"value":0.98383476,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"77","issue":"264","first_page":"2345","last_page":"2373"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11166","display_name":"Analytic Number Theory Research","score":0.9876000285148621,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9861999750137329,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8309818506240845},{"id":"https://openalex.org/keywords/extensibility","display_name":"Extensibility","score":0.7518190145492554},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.700417160987854},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.6479172110557556},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5178328156471252},{"id":"https://openalex.org/keywords/yield","display_name":"Yield (engineering)","score":0.5091971755027771},{"id":"https://openalex.org/keywords/star","display_name":"Star (game theory)","score":0.4879140555858612},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.4758412837982178},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.40760764479637146},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.151203453540802},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1096586287021637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10547822713851929},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.048570483922958374}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8309818506240845},{"id":"https://openalex.org/C32833848","wikidata":"https://www.wikidata.org/wiki/Q4115054","display_name":"Extensibility","level":2,"score":0.7518190145492554},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.700417160987854},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.6479172110557556},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5178328156471252},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.5091971755027771},{"id":"https://openalex.org/C2780897414","wikidata":"https://www.wikidata.org/wiki/Q7600592","display_name":"Star (game theory)","level":2,"score":0.4879140555858612},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.4758412837982178},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.40760764479637146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.151203453540802},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1096586287021637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10547822713851929},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.048570483922958374},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-08-02009-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02009-7","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02009-7/S0025-5718-08-02009-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-08-02009-7","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-08-02009-7","pdf_url":"https://www.ams.org/mcom/2008-77-264/S0025-5718-08-02009-7/S0025-5718-08-02009-7.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2094952117.pdf","grobid_xml":"https://content.openalex.org/works/W2094952117.grobid-xml"},"referenced_works_count":38,"referenced_works":["https://openalex.org/W98388201","https://openalex.org/W181000987","https://openalex.org/W1758500664","https://openalex.org/W1765511840","https://openalex.org/W1976544585","https://openalex.org/W1981674458","https://openalex.org/W1981743146","https://openalex.org/W1985018928","https://openalex.org/W1986280275","https://openalex.org/W1991368063","https://openalex.org/W2011200438","https://openalex.org/W2015558767","https://openalex.org/W2027669629","https://openalex.org/W2035455944","https://openalex.org/W2040396531","https://openalex.org/W2042083287","https://openalex.org/W2043419861","https://openalex.org/W2044248217","https://openalex.org/W2047253701","https://openalex.org/W2059141990","https://openalex.org/W2066783494","https://openalex.org/W2070503382","https://openalex.org/W2076597612","https://openalex.org/W2079366547","https://openalex.org/W2084898049","https://openalex.org/W2091862355","https://openalex.org/W2094899280","https://openalex.org/W2099375630","https://openalex.org/W2126004257","https://openalex.org/W2140262981","https://openalex.org/W2151084831","https://openalex.org/W2166634029","https://openalex.org/W3175367423","https://openalex.org/W4240323957","https://openalex.org/W4251085907","https://openalex.org/W4285719527","https://openalex.org/W4300580367","https://openalex.org/W4388288416"],"related_works":["https://openalex.org/W1948607442","https://openalex.org/W2808944898","https://openalex.org/W4247766898","https://openalex.org/W2044615423","https://openalex.org/W2361584951","https://openalex.org/W3004004161","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W2365327041"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"shown":[3],"by":[4,184],"Hickernell":[5],"and":[6,192],"Niederreiter":[7],"that":[8,165],"there":[9],"exist":[10],"generating":[11,92,199],"vectors":[12,93,200],"for":[13,21,58,88,98,135,198],"integration":[14,19],"lattices":[15,172],"which":[16,94,163],"yield":[17,168],"small":[18,202],"errors":[20],"<inline-formula":[22,61,99,138],"content-type=\"math/mathml\">":[23,62,100,139],"<mml:math":[24,63,101,140],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[25,64,102,141],"alttext=\"n":[26,103],"equals":[27,104],"p":[28,30,105,107],"comma":[29,32,106,109],"squared":[31,108],"ellipsis\">":[33,110],"<mml:semantics>":[34,68,111,145],"<mml:mrow>":[35,69,112,146],"<mml:mi>n</mml:mi>":[36,113],"<mml:mo>=</mml:mo>":[37,114],"<mml:mi>p</mml:mi>":[38,41,70,115,118,147],"<mml:mo>,</mml:mo>":[39,44,116,121],"<mml:msup>":[40,117],"<mml:mn>2</mml:mn>":[42,74,119,151],"</mml:msup>":[43,120],"<mml:mo>":[45,71,122,148],"\u2026":[46,123],"</mml:mo>":[47,73,124,150],"</mml:mrow>":[48,75,125,152],"<mml:annotation":[49,76,126,153],"encoding=\"application/x-tex\">n":[50,127],"=":[51,128],"p,":[52,129],"p^2,":[53,130],"\\ldots</mml:annotation>":[54,131],"</mml:semantics>":[55,80,132,157],"</mml:math>":[56,81,133,158],"</inline-formula>":[57,82,134,159],"all":[59,136],"integers":[60,137],"alttext=\"p":[65,142],"greater-than-or-equal-to":[66,143],"2\">":[67,144],"\u2265":[72,149],"encoding=\"application/x-tex\">p":[77,154],"\\ge":[78,155],"2</mml:annotation>":[79,156],".":[83,160],"This":[84],"paper":[85],"provides":[86],"algorithms":[87,167,181],"the":[89,186],"construction":[90,189],"of":[91,190],"are":[95,173,182,196],"finitely":[96],"extensible":[97,170],"The":[161],"proofs":[162],"show":[164],"our":[166],"good":[169],"rank-1":[171],"based":[174],"on":[175],"a":[176],"sieve":[177],"principle.":[178],"Particularly":[179],"fast":[180,187],"obtained":[183],"using":[185],"component-by-component":[188],"Nuyens":[191],"Cools.":[193],"Analogous":[194],"results":[195],"presented":[197],"with":[201],"weighted":[203],"star":[204],"discrepancy.":[205]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
