{"id":"https://openalex.org/W2098502274","doi":"https://doi.org/10.1017/s0963548300001905","title":"<i>t</i>-Covering Arrays: Upper Bounds and Poisson Approximations","display_name":"<i>t</i>-Covering Arrays: Upper Bounds and Poisson Approximations","publication_year":1996,"publication_date":"1996-06-01","ids":{"openalex":"https://openalex.org/W2098502274","doi":"https://doi.org/10.1017/s0963548300001905","mag":"2098502274"},"language":"en","primary_location":{"id":"doi:10.1017/s0963548300001905","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300001905","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","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/A5081970112","display_name":"Anant P. Godbole","orcid":"https://orcid.org/0000-0001-6984-3194"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anant P. Godbole","raw_affiliation_strings":["Department of Mathematical Sciences, Michigan Technological University, Houghton MI 49931, USA","Department of Mathematical Sciences, Michigan Technological University, Houghton, MI $49931$, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Michigan Technological University, Houghton MI 49931, USA","institution_ids":["https://openalex.org/I11957088"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Michigan Technological University, Houghton, MI $49931$, USA","institution_ids":["https://openalex.org/I11957088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073270142","display_name":"Daphne Skipper","orcid":"https://orcid.org/0000-0002-4683-1761"},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daphne E. Skipper","raw_affiliation_strings":["Department of Mathematics, University of Kentucky, Lexington KY 40506, USA","Department of Mathematics University of Kentucky Lexington KY 40506 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Kentucky, Lexington KY 40506, USA","institution_ids":["https://openalex.org/I143302722"]},{"raw_affiliation_string":"Department of Mathematics University of Kentucky Lexington KY 40506 USA","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042573069","display_name":"Rachel A. Sunley","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rachel A. Sunley","raw_affiliation_strings":["Department of Mathematics, University of Michigan, Ann Arbor MI 48109, USA","Department of Mathematics,  University of Michigan, Ann Arbor, MI 48109, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Michigan, Ann Arbor MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Department of Mathematics,  University of Michigan, Ann Arbor, MI 48109, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1056,"has_fulltext":false,"cited_by_count":74,"citation_normalized_percentile":{"value":0.86271451,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"5","issue":"2","first_page":"105","last_page":"117"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11797","display_name":"graph theory and CDMA systems","score":0.9919999837875366,"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/T12029","display_name":"DNA and Biological Computing","score":0.9779000282287598,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"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/combinatorics","display_name":"Combinatorics","score":0.8405613899230957},{"id":"https://openalex.org/keywords/row","display_name":"Row","score":0.832932710647583},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.6813434362411499},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6750133633613586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6565167903900146},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6409631371498108},{"id":"https://openalex.org/keywords/row-and-column-spaces","display_name":"Row and column spaces","score":0.5897698998451233},{"id":"https://openalex.org/keywords/poisson-distribution","display_name":"Poisson distribution","score":0.4633837938308716},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4212941825389862},{"id":"https://openalex.org/keywords/word","display_name":"Word (group theory)","score":0.4156649112701416},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3808063864707947},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08866024017333984},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08252942562103271},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06876781582832336},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.06505146622657776}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8405613899230957},{"id":"https://openalex.org/C135598885","wikidata":"https://www.wikidata.org/wiki/Q1366302","display_name":"Row","level":2,"score":0.832932710647583},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.6813434362411499},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6750133633613586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6565167903900146},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6409631371498108},{"id":"https://openalex.org/C104140500","wikidata":"https://www.wikidata.org/wiki/Q2088159","display_name":"Row and column spaces","level":3,"score":0.5897698998451233},{"id":"https://openalex.org/C100906024","wikidata":"https://www.wikidata.org/wiki/Q205692","display_name":"Poisson distribution","level":2,"score":0.4633837938308716},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4212941825389862},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.4156649112701416},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3808063864707947},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08866024017333984},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08252942562103271},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06876781582832336},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.06505146622657776},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"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":2,"locations":[{"id":"doi:10.1017/s0963548300001905","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0963548300001905","pdf_url":null,"source":{"id":"https://openalex.org/S7291079","display_name":"Combinatorics Probability Computing","issn_l":"0963-5483","issn":["0963-5483","1469-2163"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorics, Probability and Computing","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p-27063","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/7761","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W1510730180","https://openalex.org/W1855649115","https://openalex.org/W1989616165","https://openalex.org/W1998960351","https://openalex.org/W2017080670","https://openalex.org/W2027948337","https://openalex.org/W2036517292","https://openalex.org/W2044230505","https://openalex.org/W2068871408","https://openalex.org/W2166614386","https://openalex.org/W2798655805","https://openalex.org/W4388258552","https://openalex.org/W6649972737"],"related_works":["https://openalex.org/W2313440505","https://openalex.org/W3123744736","https://openalex.org/W2137691148","https://openalex.org/W1505848319","https://openalex.org/W4281399881","https://openalex.org/W2905020035","https://openalex.org/W3166006430","https://openalex.org/W4281971614","https://openalex.org/W2049180840","https://openalex.org/W1992086467"],"abstract_inverted_index":{"A":[0],"k\u00d7n":[1],"array":[2,68,113],"with":[3],"entries":[4],"from":[5],"the":[6,39,50,83,102,109,127,164,174,185],"q":[7,13,33,59,75,96,128],"-letter":[8],"alphabet":[9],"{0,":[10],"1,":[11],"\u2026,":[12],"\u2212":[14],"1}":[15],"is":[16,177],"said":[17],"to":[18,43,81,158,179],"be":[19],"t-covering":[20],"if":[21],"each":[22,116,125],"k":[23,170],"\u00d7":[24,171],"t":[25,34,66,71,119,129,134,161,190],"submatrix":[26],"has":[27],"(at":[28],"least":[29,136,198],"one":[30,199],"set":[31,117],"of)":[32],"distinct":[35],"rows.":[36],"We":[37],"use":[38],"Lov\u00e1sz":[40,141],"local":[41],"lemma":[42,142],"obtain":[44,180],"a":[45,65,168,181],"general":[46],"upper":[47,145],"bound":[48,146],"on":[49,147],"minimal":[51],"number":[52,104,186],"K":[53,55,88,91,148],"=":[54,72,76,90],"(":[56,93],"n,":[57,94],"t,":[58,95],")":[60],"of":[61,105,111,118,126,132,187,189],"rows":[62,106,155],"for":[63,70,114,184],"which":[64,115],"-covering":[67],"exists;":[69],"3":[73],"and":[74],"2,":[77],"we":[78],"are":[79,156,193],"able":[80],"match":[82],"best-known":[84],"such":[85],"bound.":[86],"Let":[87],"\u03bb":[89,92,137,149],"),":[97],"(\u03bb":[98],"\u2265":[99],"2),":[100],"denote":[101],"minimum":[103],"that":[107,150,192],"guarantees":[108],"existence":[110],"an":[112,144],"columns":[120,191],"contains,":[121],"amongst":[122],"its":[123],"rows,":[124],"possible":[130],"\u2018words\u2019":[131],"length":[133],"at":[135,197],"times":[138],".":[139],"The":[140],"yields":[143],"reveals":[151],"how":[152],"substantially":[153],"fewer":[154],"needed":[157],"accomplish":[159],"subsequent":[160],"-coverings":[162],"(beyond":[163],"first).":[165],"Finally,":[166],"given":[167],"random":[169],"n":[172],"array,":[173],"Stein\u2013Chen":[175],"method":[176],"employed":[178],"Poisson":[182],"approximation":[183],"sets":[188],"deficient,":[194],"i.e.":[195],"missing":[196],"word.":[200]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2016-06-24T00:00:00"}