{"id":"https://openalex.org/W1964971655","doi":"https://doi.org/10.1090/s0025-5718-00-01281-3","title":"Centered $L_2$-discrepancy of random sampling and Latin hypercubedesign, and construction of uniform designs","display_name":"Centered $L_2$-discrepancy of random sampling and Latin hypercubedesign, and construction of uniform designs","publication_year":2000,"publication_date":"2000-10-16","ids":{"openalex":"https://openalex.org/W1964971655","doi":"https://doi.org/10.1090/s0025-5718-00-01281-3","mag":"1964971655"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01281-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01281-3","pdf_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-00-01281-3/S0025-5718-00-01281-3.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-00-01281-3/S0025-5718-00-01281-3.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090862509","display_name":"Kai\u2010Tai Fang","orcid":"https://orcid.org/0000-0002-5651-5156"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I141568987","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131","country_code":"HK","type":"education","lineage":["https://openalex.org/I141568987"]}],"countries":["CN","HK"],"is_corresponding":true,"raw_author_name":"Kai-Tai Fang","raw_affiliation_strings":["Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong; and Chinese Academy of Sciences, Beijing, China","Chinese Academy of Sciences, Beijing, China","Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong; and Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I141568987"]},{"raw_affiliation_string":"Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong","institution_ids":["https://openalex.org/I141568987"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060696932","display_name":"Chang\u2010Xing Ma","orcid":"https://orcid.org/0000-0002-4696-2008"},"institutions":[{"id":"https://openalex.org/I205237279","display_name":"Nankai University","ror":"https://ror.org/01y1kjr75","country_code":"CN","type":"education","lineage":["https://openalex.org/I205237279"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chang-Xing Ma","raw_affiliation_strings":["Department of Statistics, Nankai University, Tianjin, China"],"affiliations":[{"raw_affiliation_string":"Department of Statistics, Nankai University, Tianjin, China","institution_ids":["https://openalex.org/I205237279"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5086357086","display_name":"Peter Winker","orcid":"https://orcid.org/0000-0003-3412-4207"},"institutions":[{"id":"https://openalex.org/I177802217","display_name":"University of Mannheim","ror":"https://ror.org/031bsb921","country_code":"DE","type":"education","lineage":["https://openalex.org/I177802217"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Peter Winker","raw_affiliation_strings":["Department of Economics, University of Mannheim, 68131 Mannheim, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Economics, University of Mannheim, 68131 Mannheim, Germany","institution_ids":["https://openalex.org/I177802217"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090862509"],"corresponding_institution_ids":["https://openalex.org/I141568987","https://openalex.org/I19820366"],"apc_list":null,"apc_paid":null,"fwci":4.2203,"has_fulltext":true,"cited_by_count":188,"citation_normalized_percentile":{"value":0.94351687,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"71","issue":"237","first_page":"275","last_page":"297"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9979000091552734,"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":0.9979000091552734,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11159","display_name":"Manufacturing Process and Optimization","score":0.9735000133514404,"subfield":{"id":"https://openalex.org/subfields/2209","display_name":"Industrial and Manufacturing Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/latin-hypercube-sampling","display_name":"Latin hypercube sampling","score":0.9616707563400269},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.772829532623291},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6230033040046692},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.604137122631073},{"id":"https://openalex.org/keywords/equidistant","display_name":"Equidistant","score":0.5647514462471008},{"id":"https://openalex.org/keywords/heuristic","display_name":"Heuristic","score":0.5448569655418396},{"id":"https://openalex.org/keywords/hypercube","display_name":"Hypercube","score":0.5235280990600586},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5006580352783203},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42185673117637634},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3259648084640503},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.32524484395980835},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.27339476346969604},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.2600267231464386},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.18685272336006165},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17828193306922913},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07541370391845703}],"concepts":[{"id":"https://openalex.org/C20820323","wikidata":"https://www.wikidata.org/wiki/Q6496514","display_name":"Latin hypercube sampling","level":3,"score":0.9616707563400269},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.772829532623291},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6230033040046692},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.604137122631073},{"id":"https://openalex.org/C158245278","wikidata":"https://www.wikidata.org/wiki/Q4386982","display_name":"Equidistant","level":2,"score":0.5647514462471008},{"id":"https://openalex.org/C173801870","wikidata":"https://www.wikidata.org/wiki/Q201413","display_name":"Heuristic","level":2,"score":0.5448569655418396},{"id":"https://openalex.org/C50820777","wikidata":"https://www.wikidata.org/wiki/Q213723","display_name":"Hypercube","level":2,"score":0.5235280990600586},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5006580352783203},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42185673117637634},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3259648084640503},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.32524484395980835},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27339476346969604},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.2600267231464386},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.18685272336006165},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17828193306922913},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07541370391845703},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1090/s0025-5718-00-01281-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01281-3","pdf_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-00-01281-3/S0025-5718-00-01281-3.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.8255","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.8255","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2002-71-237/S0025-5718-00-01281-3/S0025-5718-00-01281-3.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.4302","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.4302","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://math.hkbu.edu.hk/pub/techreport/math233.ps.gz","raw_type":"text"},{"id":"pmh:oai:ub-madoc.bib.uni-mannheim.de:10681","is_oa":false,"landing_page_url":"http://www.ams.org/journals/mcom/2002-71-237/S0025-5718-00-01281-3/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196315","display_name":"MADOC (University of Mannheim)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177802217","host_organization_name":"University of Mannheim","host_organization_lineage":["https://openalex.org/I177802217"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Zeitschriftenartikel"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-00-01281-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01281-3","pdf_url":"https://www.ams.org/mcom/2002-71-237/S0025-5718-00-01281-3/S0025-5718-00-01281-3.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":null,"license_id":null,"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/F4320320955","display_name":"Hong Kong Baptist University","ror":"https://ror.org/0145fw131"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1964971655.pdf","grobid_xml":"https://content.openalex.org/works/W1964971655.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W936536805","https://openalex.org/W1533955387","https://openalex.org/W1967692477","https://openalex.org/W1968648452","https://openalex.org/W2016871238","https://openalex.org/W2038669746","https://openalex.org/W2040396531","https://openalex.org/W2043419861","https://openalex.org/W2051591670","https://openalex.org/W2145811598","https://openalex.org/W2151025666","https://openalex.org/W2162423772","https://openalex.org/W2253807580","https://openalex.org/W2318856246","https://openalex.org/W2331011396","https://openalex.org/W2611147641","https://openalex.org/W4230160500","https://openalex.org/W4243645092","https://openalex.org/W4245516440","https://openalex.org/W4285719527","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W2291164072","https://openalex.org/W2132031653","https://openalex.org/W2061718957","https://openalex.org/W2161621187","https://openalex.org/W3122806506","https://openalex.org/W2313927419","https://openalex.org/W2040716894","https://openalex.org/W1964971655","https://openalex.org/W1548110607","https://openalex.org/W2046879700"],"abstract_inverted_index":{"In":[0],"this":[1,23],"paper":[2],"properties":[3],"and":[4,20,30,36,94],"construction":[5],"of":[6,12,22,38,47,62],"designs":[7,29,41,66,89],"under":[8],"a":[9,60],"centered":[10],"version":[11],"the":[13,54,81],"$L_2$-discrepancy":[14],"are":[15,25,42],"analyzed.":[16],"The":[17,34],"theoretic":[18,92],"expectation":[19,35,93],"variance":[21,37],"discrepancy":[24,88],"derived":[26],"for":[27],"random":[28,48],"Latin":[31,39],"hypercube":[32,40],"designs.":[33,49],"significantly":[43],"lower":[44],"than":[45],"that":[46],"While":[50],"in":[51,67],"dimension":[52,69],"one":[53],"unique":[55],"uniform":[56],"design":[57],"is":[58,78],"also":[59],"set":[61],"equidistant":[63],"points,":[64],"low-discrepancy":[65],"higher":[68],"have":[70],"to":[71,91],"be":[72],"generated":[73],"by":[74],"explicit":[75],"optimization.":[76],"Optimization":[77],"performed":[79],"using":[80],"threshold":[82],"accepting":[83],"heuristic":[84],"which":[85],"produces":[86],"low":[87],"compared":[90],"variance.":[95]},"counts_by_year":[{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":12},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":15},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}