{"id":"https://openalex.org/W4405530835","doi":"https://doi.org/10.3390/sym16121678","title":"Implementing the MOLS Table for n Up to 500","display_name":"Implementing the MOLS Table for n Up to 500","publication_year":2024,"publication_date":"2024-12-18","ids":{"openalex":"https://openalex.org/W4405530835","doi":"https://doi.org/10.3390/sym16121678"},"language":"en","primary_location":{"id":"doi:10.3390/sym16121678","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121678","pdf_url":"https://www.mdpi.com/2073-8994/16/12/1678/pdf?version=1734531309","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/16/12/1678/pdf?version=1734531309","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5014891009","display_name":"Alice Miller","orcid":"https://orcid.org/0000-0002-0941-1717"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Alice Miller","raw_affiliation_strings":["School of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK"],"raw_orcid":"https://orcid.org/0000-0002-0941-1717","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021994297","display_name":"R. Julian R. Abel","orcid":"https://orcid.org/0000-0002-3632-9612"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"R. Julian R. Abel","raw_affiliation_strings":["School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia"],"raw_orcid":"https://orcid.org/0000-0002-3632-9612","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077791466","display_name":"Ivaylo Valkov","orcid":"https://orcid.org/0000-0003-1116-875X"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ivaylo Valkov","raw_affiliation_strings":["School of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK"],"raw_orcid":"https://orcid.org/0000-0003-1116-875X","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016771048","display_name":"Douglas Fraser","orcid":"https://orcid.org/0009-0008-5291-6519"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Douglas Fraser","raw_affiliation_strings":["School of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK"],"raw_orcid":"https://orcid.org/0009-0008-5291-6519","affiliations":[{"raw_affiliation_string":"School of Computing Science, University of Glasgow, Glasgow G12 8QQ, UK","institution_ids":["https://openalex.org/I7882870"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5014891009"],"corresponding_institution_ids":["https://openalex.org/I7882870"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20112738,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"12","first_page":"1678","last_page":"1678"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":1.0,"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":1.0,"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":0.9739999771118164,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9186999797821045,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/permutation","display_name":"Permutation (music)","score":0.6782722473144531},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6515430212020874},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.6270963549613953},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.5124931335449219},{"id":"https://openalex.org/keywords/latin-square","display_name":"Latin square","score":0.5089209079742432},{"id":"https://openalex.org/keywords/scheduling","display_name":"Scheduling (production processes)","score":0.4644833207130432},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.45532017946243286},{"id":"https://openalex.org/keywords/orthogonal-array","display_name":"Orthogonal array","score":0.4374958276748657},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4137415289878845},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36329054832458496},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.341715931892395},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.31182295083999634},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.29096633195877075},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17220786213874817},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.1709895133972168},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09462791681289673},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.06537207961082458}],"concepts":[{"id":"https://openalex.org/C21308566","wikidata":"https://www.wikidata.org/wiki/Q7169365","display_name":"Permutation (music)","level":2,"score":0.6782722473144531},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6515430212020874},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.6270963549613953},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.5124931335449219},{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.5089209079742432},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.4644833207130432},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.45532017946243286},{"id":"https://openalex.org/C42632107","wikidata":"https://www.wikidata.org/wiki/Q2031860","display_name":"Orthogonal array","level":3,"score":0.4374958276748657},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4137415289878845},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36329054832458496},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.341715931892395},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31182295083999634},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29096633195877075},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17220786213874817},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.1709895133972168},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09462791681289673},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.06537207961082458},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C70262065","wikidata":"https://www.wikidata.org/wiki/Q427652","display_name":"Rumen","level":3,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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/C83469408","wikidata":"https://www.wikidata.org/wiki/Q2036525","display_name":"Taguchi methods","level":2,"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/C31903555","wikidata":"https://www.wikidata.org/wiki/Q1637030","display_name":"Food science","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym16121678","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121678","pdf_url":"https://www.mdpi.com/2073-8994/16/12/1678/pdf?version=1734531309","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:eprints.gla.ac.uk:343648","is_oa":true,"landing_page_url":"http://eprints.gla.ac.uk/view/author/1503.html>","pdf_url":"https://eprints.gla.ac.uk/343648/1/343648.pdf","source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"},{"id":"pmh:oai:doaj.org/article:64fbf99beb4b4217a61f68bcc8d58a16","is_oa":false,"landing_page_url":"https://doaj.org/article/64fbf99beb4b4217a61f68bcc8d58a16","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 16, Iss 12, p 1678 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym16121678","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym16121678","pdf_url":"https://www.mdpi.com/2073-8994/16/12/1678/pdf?version=1734531309","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1849282983","display_name":null,"funder_award_id":"RF-2024-116","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G2327885119","display_name":null,"funder_award_id":"EP/V519686/1","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"},{"id":"https://openalex.org/G2849512009","display_name":null,"funder_award_id":"RF-2024-116","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G6041577085","display_name":"Industrial CASE Account - University of Glasgow 2020","funder_award_id":"EP/V519686/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320320337","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405530835.pdf","grobid_xml":"https://content.openalex.org/works/W4405530835.grobid-xml"},"referenced_works_count":73,"referenced_works":["https://openalex.org/W634359228","https://openalex.org/W1487647779","https://openalex.org/W1526492230","https://openalex.org/W1557333724","https://openalex.org/W1560023680","https://openalex.org/W1565202964","https://openalex.org/W1832221442","https://openalex.org/W1843403350","https://openalex.org/W1957100706","https://openalex.org/W1965142549","https://openalex.org/W1975150539","https://openalex.org/W1976677460","https://openalex.org/W1979552258","https://openalex.org/W1981295236","https://openalex.org/W1985957440","https://openalex.org/W1987701799","https://openalex.org/W2000020745","https://openalex.org/W2001496048","https://openalex.org/W2001542594","https://openalex.org/W2014997640","https://openalex.org/W2023506731","https://openalex.org/W2029376662","https://openalex.org/W2030340273","https://openalex.org/W2041054306","https://openalex.org/W2044022598","https://openalex.org/W2044321413","https://openalex.org/W2046272424","https://openalex.org/W2055207311","https://openalex.org/W2060812201","https://openalex.org/W2062944227","https://openalex.org/W2064451160","https://openalex.org/W2066218472","https://openalex.org/W2069903885","https://openalex.org/W2071498995","https://openalex.org/W2072206178","https://openalex.org/W2074214232","https://openalex.org/W2080625978","https://openalex.org/W2080856338","https://openalex.org/W2080872158","https://openalex.org/W2083478276","https://openalex.org/W2104413285","https://openalex.org/W2124016695","https://openalex.org/W2148602768","https://openalex.org/W2150206873","https://openalex.org/W2156872656","https://openalex.org/W2168287084","https://openalex.org/W2320377306","https://openalex.org/W2322839632","https://openalex.org/W2332640733","https://openalex.org/W2742142194","https://openalex.org/W2751256703","https://openalex.org/W2752462646","https://openalex.org/W2885382897","https://openalex.org/W2922092909","https://openalex.org/W2964326359","https://openalex.org/W3101256766","https://openalex.org/W3103049906","https://openalex.org/W3118083443","https://openalex.org/W4205545339","https://openalex.org/W4205570794","https://openalex.org/W4231874819","https://openalex.org/W4241311033","https://openalex.org/W4241580894","https://openalex.org/W4254866411","https://openalex.org/W6633184379","https://openalex.org/W6633356086","https://openalex.org/W6633702648","https://openalex.org/W6741975064","https://openalex.org/W6743492043","https://openalex.org/W6743613031","https://openalex.org/W6801076681","https://openalex.org/W6833700903","https://openalex.org/W6964917394"],"related_works":["https://openalex.org/W2393403800","https://openalex.org/W2044829724","https://openalex.org/W169006039","https://openalex.org/W2364512413","https://openalex.org/W2326647168","https://openalex.org/W2042914544","https://openalex.org/W2390590114","https://openalex.org/W4388328977","https://openalex.org/W2376096933","https://openalex.org/W4389478513"],"abstract_inverted_index":{"Latin":[0,36],"squares":[1,37],"are":[2,40,50,53],"an":[3],"essential":[4],"tool":[5],"in":[6],"the":[7,28,76,101,109],"construction":[8],"of":[9,33,47,59,80,82,118,120],"combinatorial":[10],"designs.":[11],"Optimal":[12],"solutions":[13],"for":[14,23,85,94,100,115],"problems":[15,19],"such":[16],"as":[17,41,43],"scheduling":[18],"and":[20,61,68,104],"permutation":[21],"arrays":[22],"powerline":[24],"communication":[25],"rely":[26],"on":[27],"ability":[29],"to":[30,66,88],"construct":[31],"sets":[32,49,79,117],"mutually":[34],"orthogonal":[35],"(MOLS)":[38],"that":[39],"large":[42],"possible.":[44],"Although":[45],"constructions":[46,114],"suitable":[48],"known,":[51],"they":[52],"scattered":[54],"among":[55],"a":[56,92],"wide":[57],"variety":[58],"sources,":[60],"can":[62],"be":[63],"both":[64],"difficult":[65,102],"understand":[67],"contain":[69],"errors.":[70],"We":[71,90,111],"describe":[72],"our":[73],"experience":[74],"implementing":[75],"largest":[77],"known":[78],"MOLS":[81,119],"order":[83,121],"n,":[84,122],"n":[86,124],"up":[87],"500.":[89],"give":[91,113],"source":[93],"each":[95],"construction,":[96],"provide":[97],"additional":[98],"hints":[99],"cases,":[103],"correct":[105],"some":[106],"errors":[107],"along":[108],"way.":[110],"also":[112],"new":[116],"where":[123],"is":[125],"486,":[126],"567,":[127],"622,":[128],"635,":[129],"754,":[130],"756,":[131],"764,":[132],"766,":[133],"774,":[134],"778,":[135],"802,":[136],"810,":[137],"822,":[138],"826,":[139],"894,":[140],"906,":[141],"916,":[142],"920":[143],"or":[144],"936.":[145]},"counts_by_year":[],"updated_date":"2026-05-21T09:19:25.381259","created_date":"2025-10-10T00:00:00"}