{"id":"https://openalex.org/W2949920420","doi":"https://doi.org/10.1080/03610918.2019.1628988","title":"Some interesting behaviors of good lattice point sets","display_name":"Some interesting behaviors of good lattice point sets","publication_year":2019,"publication_date":"2019-06-20","ids":{"openalex":"https://openalex.org/W2949920420","doi":"https://doi.org/10.1080/03610918.2019.1628988","mag":"2949920420"},"language":"en","primary_location":{"id":"doi:10.1080/03610918.2019.1628988","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1628988","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051205038","display_name":"A. M. Elsawah","orcid":"https://orcid.org/0000-0001-6116-4779"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I192398990","display_name":"Zagazig University","ror":"https://ror.org/053g6we49","country_code":"EG","type":"education","lineage":["https://openalex.org/I192398990"]}],"countries":["CN","EG"],"is_corresponding":true,"raw_author_name":"A. M. Elsawah","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt","Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China"],"raw_orcid":"https://orcid.org/0000-0001-6116-4779","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt","institution_ids":["https://openalex.org/I192398990"]},{"raw_affiliation_string":"Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China","institution_ids":["https://openalex.org/I12615008"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090862509","display_name":"Kai\u2010Tai Fang","orcid":"https://orcid.org/0000-0002-5651-5156"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai-Tai Fang","raw_affiliation_strings":["Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China","The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China","institution_ids":["https://openalex.org/I12615008"]},{"raw_affiliation_string":"The Key Lab of Random Complex Structures and Data Analysis, The Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101898906","display_name":"Yuhui Deng","orcid":"https://orcid.org/0009-0009-5090-6349"},"institutions":[{"id":"https://openalex.org/I12615008","display_name":"Beijing Normal-Hong Kong Baptist University","ror":"https://ror.org/04snvc712","country_code":"CN","type":"education","lineage":["https://openalex.org/I12615008"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu Hui Deng","raw_affiliation_strings":["Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China","institution_ids":["https://openalex.org/I12615008"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051205038"],"corresponding_institution_ids":["https://openalex.org/I12615008","https://openalex.org/I192398990"],"apc_list":null,"apc_paid":null,"fwci":0.3245,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.5298988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"50","issue":"11","first_page":"3650","last_page":"3668"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9998999834060669,"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":0.9998999834060669,"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12176","display_name":"Optimization and Packing Problems","score":0.9904000163078308,"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.603271484375},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.5869472026824951},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.5275475382804871},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4671577513217926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46224427223205566},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43649184703826904},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.41921812295913696},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.41717177629470825},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40201079845428467},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34713369607925415},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.182127445936203}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.603271484375},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.5869472026824951},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.5275475382804871},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4671577513217926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46224427223205566},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43649184703826904},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.41921812295913696},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.41717177629470825},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40201079845428467},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34713369607925415},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.182127445936203},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/03610918.2019.1628988","is_oa":false,"landing_page_url":"https://doi.org/10.1080/03610918.2019.1628988","pdf_url":null,"source":{"id":"https://openalex.org/S153329750","display_name":"Communications in Statistics - Simulation and Computation","issn_l":"0361-0918","issn":["0361-0918","1532-4141"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Statistics - Simulation and Computation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5400000214576721,"id":"https://metadata.un.org/sdg/12","display_name":"Responsible consumption and production"}],"awards":[{"id":"https://openalex.org/G2007378359","display_name":null,"funder_award_id":"R201912","funder_id":"https://openalex.org/F4320332697","funder_display_name":"University of Illinois at Chicago"},{"id":"https://openalex.org/G7019194043","display_name":null,"funder_award_id":"R201712","funder_id":"https://openalex.org/F4320332697","funder_display_name":"University of Illinois at Chicago"},{"id":"https://openalex.org/G7134875993","display_name":null,"funder_award_id":"R201810","funder_id":"https://openalex.org/F4320332697","funder_display_name":"University of Illinois at Chicago"}],"funders":[{"id":"https://openalex.org/F4320332697","display_name":"University of Illinois at Chicago","ror":"https://ror.org/02mpq6x41"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1589492117","https://openalex.org/W1976544585","https://openalex.org/W2085002359","https://openalex.org/W2232720629","https://openalex.org/W2294006238","https://openalex.org/W2622813076","https://openalex.org/W2895503911","https://openalex.org/W4210441770","https://openalex.org/W4238205818","https://openalex.org/W4300580367"],"related_works":["https://openalex.org/W4281971614","https://openalex.org/W2390933768","https://openalex.org/W2467236363","https://openalex.org/W3125750421","https://openalex.org/W3175260668","https://openalex.org/W3122721839","https://openalex.org/W2953259538","https://openalex.org/W2184455175","https://openalex.org/W2292909562","https://openalex.org/W2557298224"],"abstract_inverted_index":{"Good":[0],"lattice":[1],"point":[2],"(GLP)":[3],"sets":[4,6,25],"are":[5,10,26,74,88,194],"of":[7,16,30,47,58,70,115,125,129,162,166,191,212],"points":[8,31],"that":[9,67],"uniformly":[11],"distributed":[12],"over":[13],"the":[14,56,68,77,97,111,119,127,130,145,163,172],"domain":[15],"interest":[17],"and":[18,45,100,105,170,177,187],"thus":[19],"have":[20],"good":[21],"space-filling":[22],"property.":[23],"GLP":[24,59,72,78,131,168,205,213],"an":[27],"important":[28],"kind":[29],"for":[32,148,201],"many":[33],"applications,":[34],"such":[35],"as":[36,198],"multidimensional":[37],"quadrature,":[38],"simulation,":[39],"computer":[40],"experiments,":[41],"quasi-Monte":[42],"Carlo":[43],"techniques":[44],"design":[46],"experiments.":[48],"It":[49,140],"is":[50,141],"a":[51,71,199],"significant":[52,151],"issue":[53],"to":[54,143],"study":[55],"behaviors":[57,161],"sets.":[60,214],"For":[61],"instance,":[62],"most":[63],"real-life":[64],"applications":[65,211],"require":[66],"columns":[69,87,178],"set":[73,79,132,169],"independent,":[75],"i.e.,":[76],"has":[80],"full":[81,203],"rank.":[82],"If":[83],"one":[84],"or":[85],"more":[86,94],"linearly":[89],"dependent,":[90],"there":[91],"will":[92],"be":[93],"confounding":[95],"among":[96,174,184],"main":[98],"effects":[99],"interactions":[101],"in":[102,118,138,209],"statistical":[103],"models":[104],"also":[106,208],"we":[107],"can":[108],"not":[109,196],"find":[110],"least":[112],"squares":[113],"estimation":[114],"regression":[116,121],"coefficients":[117],"linear":[120],"model.":[122],"The":[123,189],"problem":[124],"finding":[126],"rank":[128,204],"remained":[133],"unsolved":[134],"since":[135],"its":[136,175],"inception":[137],"1959.":[139],"desirable":[142],"put":[144],"first":[146],"stone":[147],"solving":[149],"this":[150,156,192],"problem.":[152],"Through":[153],"theoretical":[154],"justifications,":[155],"paper":[157,193],"gives":[158],"some":[159,181],"interesting":[160],"generating":[164],"vector":[165],"any":[167],"shows":[171],"independence":[173],"rows":[176,186],"by":[179],"presenting":[180],"analytic":[182],"linkages":[183],"these":[185],"columns.":[188],"results":[190],"used":[195],"only":[197],"benchmark":[200],"constructing":[202],"sets,":[206],"but":[207],"various":[210]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
