{"id":"https://openalex.org/W2503998605","doi":"https://doi.org/10.37236/6338","title":"Orthogonal Trades in Complete Sets of MOLS","display_name":"Orthogonal Trades in Complete Sets of MOLS","publication_year":2017,"publication_date":"2017-07-28","ids":{"openalex":"https://openalex.org/W2503998605","doi":"https://doi.org/10.37236/6338","mag":"2503998605"},"language":"en","primary_location":{"id":"doi:10.37236/6338","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6338","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.37236/6338","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080083927","display_name":"Nicholas J. Cavenagh","orcid":"https://orcid.org/0000-0002-9151-3842"},"institutions":[{"id":"https://openalex.org/I52179390","display_name":"University of Waikato","ror":"https://ror.org/013fsnh78","country_code":"NZ","type":"education","lineage":["https://openalex.org/I52179390"]}],"countries":["NZ"],"is_corresponding":true,"raw_author_name":"Nicholas Cavenagh","raw_affiliation_strings":["Waikato University"],"affiliations":[{"raw_affiliation_string":"Waikato University","institution_ids":["https://openalex.org/I52179390"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079580434","display_name":"Diane Donovan","orcid":"https://orcid.org/0000-0002-1329-3514"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Diane Donovan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039667459","display_name":"Fatih Demirkale","orcid":"https://orcid.org/0000-0002-6114-1291"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fatih Demirkale","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080083927"],"corresponding_institution_ids":["https://openalex.org/I52179390"],"apc_list":null,"apc_paid":null,"fwci":0.1433,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.46861078,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"24","issue":"3","first_page":null,"last_page":null},"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":0.9674000144004822,"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/T10849","display_name":"Finite Group Theory Research","score":0.9372000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8721434473991394},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.857298731803894},{"id":"https://openalex.org/keywords/orthogonality","display_name":"Orthogonality","score":0.8208146095275879},{"id":"https://openalex.org/keywords/latin-square","display_name":"Latin square","score":0.6760152578353882},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.614464282989502},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.6128494739532471},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.596916675567627},{"id":"https://openalex.org/keywords/transversal","display_name":"Transversal (combinatorics)","score":0.58589106798172},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.5722535848617554},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.5626883506774902},{"id":"https://openalex.org/keywords/square","display_name":"Square (algebra)","score":0.5297314524650574},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.47054344415664673},{"id":"https://openalex.org/keywords/main-diagonal","display_name":"Main diagonal","score":0.4402925372123718},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38173508644104004},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06613963842391968}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8721434473991394},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.857298731803894},{"id":"https://openalex.org/C17137986","wikidata":"https://www.wikidata.org/wiki/Q215067","display_name":"Orthogonality","level":2,"score":0.8208146095275879},{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.6760152578353882},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.614464282989502},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.6128494739532471},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.596916675567627},{"id":"https://openalex.org/C2780130068","wikidata":"https://www.wikidata.org/wiki/Q2208651","display_name":"Transversal (combinatorics)","level":2,"score":0.58589106798172},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.5722535848617554},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5626883506774902},{"id":"https://openalex.org/C135692309","wikidata":"https://www.wikidata.org/wiki/Q111124","display_name":"Square (algebra)","level":2,"score":0.5297314524650574},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.47054344415664673},{"id":"https://openalex.org/C60761296","wikidata":"https://www.wikidata.org/wiki/Q651480","display_name":"Main diagonal","level":3,"score":0.4402925372123718},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38173508644104004},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06613963842391968},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C70262065","wikidata":"https://www.wikidata.org/wiki/Q427652","display_name":"Rumen","level":3,"score":0.0},{"id":"https://openalex.org/C100544194","wikidata":"https://www.wikidata.org/wiki/Q41760","display_name":"Fermentation","level":2,"score":0.0},{"id":"https://openalex.org/C31903555","wikidata":"https://www.wikidata.org/wiki/Q1637030","display_name":"Food science","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6338","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6338","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/6338","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6338","pdf_url":null,"source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4301035415","https://openalex.org/W2045112111","https://openalex.org/W2952546219","https://openalex.org/W2557059219","https://openalex.org/W4287199920","https://openalex.org/W3158379883","https://openalex.org/W4289693682","https://openalex.org/W3005351221","https://openalex.org/W2322205785","https://openalex.org/W2967987125"],"abstract_inverted_index":{"Let":[0],"$B_p$":[1,28,116,144],"be":[2],"the":[3,8,12,22,35,40,51,63,82,91,96,118,134],"Latin":[4,25,138],"square":[5,139],"given":[6,38],"by":[7,39,105],"addition":[9],"table":[10],"for":[11,47,62,81],"integers":[13],"modulo":[14],"an":[15,75],"odd":[16],"prime":[17],"$p$.":[18],"Here":[19],"we":[20,132],"consider":[21],"properties":[23],"of":[24,34,50,65,79,84,93,95,136],"trades":[26,89],"in":[27,60,70,115],"which":[29,99,140,146],"preserve":[30],"orthogonality":[31],"with":[32,74],"one":[33],"$p-1$":[36],"MOLS":[37],"finite":[41],"field":[42],"construction.":[43],"We":[44,109],"show":[45,111,133],"that":[46,112],"certain":[48],"choices":[49],"orthogonal":[52,142],"mate,":[53],"there":[54],"is":[55,141],"a":[56,72,86,102,106,137,148],"lower":[57,77],"bound":[58,78],"logarithmic":[59],"$p$":[61,122],"number":[64],"times":[66],"each":[67],"symbol":[68],"occurs":[69],"such":[71,85],"trade,":[73],"overall":[76],"$(\\log{p})^2/\\log\\log{p}$":[80],"size":[83],"trade.":[87],"Such":[88],"imply":[90],"existence":[92,135],"orthomorphisms":[94],"cyclic":[97],"group":[98],"differ":[100],"from":[101],"linear":[103],"orthomorphism":[104],"small":[107],"amount.":[108],"also":[110],"any":[113],"transversal":[114],"hits":[117],"main":[119],"diagonal":[120],"either":[121],"or":[123],"at":[124],"most":[125],"$p-\\log_2{p}-1$":[126],"times.":[127],"Finally,":[128],"if":[129],"$p\\equiv":[130],"1\\pmod{6}$":[131],"to":[143],"and":[145],"contains":[147],"$2\\times":[149],"2$":[150],"subsquare.":[151]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
