{"id":"https://openalex.org/W2010431671","doi":"https://doi.org/10.1137/s0895480101387364","title":"The Existence of 2\u00d74 Grid-Block Designs and Their Applications","display_name":"The Existence of 2\u00d74 Grid-Block Designs and Their Applications","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2010431671","doi":"https://doi.org/10.1137/s0895480101387364","mag":"2010431671"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480101387364","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480101387364","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5020499546","display_name":"Yukiyasu Mutoh","orcid":null},"institutions":[{"id":"https://openalex.org/I203951103","display_name":"Keio University","ror":"https://ror.org/02kn6nx58","country_code":"JP","type":"education","lineage":["https://openalex.org/I203951103"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yukiyasu Mutoh","raw_affiliation_strings":["Keio Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Keio Univ","institution_ids":["https://openalex.org/I203951103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049749403","display_name":"Toshio Morihara","orcid":null},"institutions":[{"id":"https://openalex.org/I203951103","display_name":"Keio University","ror":"https://ror.org/02kn6nx58","country_code":"JP","type":"education","lineage":["https://openalex.org/I203951103"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Toshio Morihara","raw_affiliation_strings":["Keio Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Keio Univ","institution_ids":["https://openalex.org/I203951103"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112260612","display_name":"Masakazu Jimbo","orcid":null},"institutions":[{"id":"https://openalex.org/I203951103","display_name":"Keio University","ror":"https://ror.org/02kn6nx58","country_code":"JP","type":"education","lineage":["https://openalex.org/I203951103"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Masakazu Jimbo","raw_affiliation_strings":["Keio Univ"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Keio Univ","institution_ids":["https://openalex.org/I203951103"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008893362","display_name":"Hung\u2010Lin Fu","orcid":"https://orcid.org/0000-0001-7218-3043"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hung-Lin Fu","raw_affiliation_strings":["Department of Applied Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7085,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71565334,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"16","issue":"2","first_page":"173","last_page":"178"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.991599977016449,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11213","display_name":"Genomic variations and chromosomal abnormalities","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/1311","display_name":"Genetics"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7758762240409851},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.7697683572769165},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.7476069331169128},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6996625661849976},{"id":"https://openalex.org/keywords/block-design","display_name":"Block design","score":0.5731766223907471},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5351138114929199},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45436790585517883},{"id":"https://openalex.org/keywords/square-tiling","display_name":"Square tiling","score":0.4140043258666992},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18398720026016235},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.11757069826126099}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7758762240409851},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.7697683572769165},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.7476069331169128},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6996625661849976},{"id":"https://openalex.org/C689293","wikidata":"https://www.wikidata.org/wiki/Q751484","display_name":"Block design","level":2,"score":0.5731766223907471},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5351138114929199},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45436790585517883},{"id":"https://openalex.org/C178650486","wikidata":"https://www.wikidata.org/wiki/Q1128619","display_name":"Square tiling","level":3,"score":0.4140043258666992},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18398720026016235},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11757069826126099},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0895480101387364","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480101387364","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","score":0.7699999809265137,"display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1544735579","https://openalex.org/W1992397972","https://openalex.org/W1999371557","https://openalex.org/W2051968426","https://openalex.org/W2078114840","https://openalex.org/W2082207918","https://openalex.org/W2103915303","https://openalex.org/W2611298788","https://openalex.org/W4210440243"],"related_works":["https://openalex.org/W2027766700","https://openalex.org/W2174875404","https://openalex.org/W1589038253","https://openalex.org/W2087235072","https://openalex.org/W337150621","https://openalex.org/W2335430869","https://openalex.org/W1516369391","https://openalex.org/W2017436447","https://openalex.org/W2921351362","https://openalex.org/W2785574196"],"abstract_inverted_index":{"Fu,":[0],"Hwang,":[1],"Jimbo,":[2],"Mutoh,":[3],"and":[4,61,93],"Shiue":[5],"[J.":[6],"Statist.":[7],"Plann.":[8],"Inference,":[9],"to":[10],"appear]":[11],"introduced":[12],"the":[13,69,74,82,95,102,136],"concept":[14],"of":[15,34,84,97,104,138],"a":[16,25,32],"grid-block":[17,99,106,140],"design,":[18],"which":[19],"is":[20,48],"defined":[21],"as":[22],"follows:":[23],"For":[24],"v-set":[26],"V,":[27],"let":[28],"${\\cal":[29],"A}$":[30],"be":[31],"collection":[33],"r":[35,51],"\u00d7":[36,52],"c":[37],"arrays":[38],"with":[39],"elements":[40],"in":[41,63,68,73],"V.":[42],"A":[43],"pair":[44],"$(V,":[45],"{\\cal":[46],"A})$":[47],"called":[49],"an":[50],"cgrid-block":[53],"design":[54,78],"if":[55],"every":[56],"two":[57],"distinct":[58],"points":[59],"i":[60],"j":[62],"V":[64],"occur":[65],"exactly":[66],"once":[67],"same":[70,75],"row":[71],"or":[72],"column.":[76],"This":[77],"has":[79],"originated":[80],"from":[81],"use":[83],"DNA":[85],"library":[86],"screening.":[87],"They":[88],"gave":[89],"some":[90],"general":[91],"constructions":[92],"proved":[94],"existence":[96,103,137],"3\u00d73":[98],"designs.":[100,141],"Meanwhile,":[101],"2\u00d73":[105],"designs":[107],"was":[108],"shown":[109],"by":[110,125],"Carter":[111],"[":[112],"Designs":[113],"on":[114],"Cubic":[115],"Multigraphs,":[116],"Ph.D.":[117],"thesis,":[118],"McMaster":[119],"University,":[120],"Hamilton,":[121],"ON,":[122],"Canada,":[123],"1989]":[124],"decomposing":[126],"Kv":[127],"into":[128],"cubic":[129],"graphs.":[130],"In":[131],"this":[132],"paper,":[133],"we":[134],"show":[135],"2\u00d74":[139]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
