{"id":"https://openalex.org/W4410815247","doi":"https://doi.org/10.1007/s10623-025-01629-5","title":"Improvements for lower bounds of mutually orthogonal Latin squares of sizes 54, 96 and 108","display_name":"Improvements for lower bounds of mutually orthogonal Latin squares of sizes 54, 96 and 108","publication_year":2025,"publication_date":"2025-05-28","ids":{"openalex":"https://openalex.org/W4410815247","doi":"https://doi.org/10.1007/s10623-025-01629-5"},"language":"en","primary_location":{"id":"doi:10.1007/s10623-025-01629-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01629-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01629-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01629-5.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","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":true,"raw_author_name":"R. Julian R. Abel","raw_affiliation_strings":["School of Mathematics and Statistics, UNSW Sydney, NSW 2052, Sydney, Australia"],"raw_orcid":"https://orcid.org/0000-0002-3632-9612","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, UNSW Sydney, NSW 2052, Sydney, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014818978","display_name":"Ingo Janiszczak","orcid":"https://orcid.org/0000-0002-4892-1189"},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ingo Janiszczak","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen, 45127, Essen, Germany"],"raw_orcid":"https://orcid.org/0000-0002-4892-1189","affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen, 45127, Essen, Germany","institution_ids":["https://openalex.org/I62318514"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017662338","display_name":"Reiner Staszewski","orcid":null},"institutions":[{"id":"https://openalex.org/I62318514","display_name":"University of Duisburg-Essen","ror":"https://ror.org/04mz5ra38","country_code":"DE","type":"education","lineage":["https://openalex.org/I62318514"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Reiner Staszewski","raw_affiliation_strings":["Faculty of Mathematics, University of Duisburg-Essen, 45127, Essen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of Duisburg-Essen, 45127, Essen, Germany","institution_ids":["https://openalex.org/I62318514"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021994297"],"corresponding_institution_ids":["https://openalex.org/I31746571"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.07072324,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"93","issue":"9","first_page":"3565","last_page":"3573"},"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/T12923","display_name":"Digital Image Processing Techniques","score":0.9855999946594238,"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/T10849","display_name":"Finite Group Theory Research","score":0.9606000185012817,"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":0.8638970851898193},{"id":"https://openalex.org/keywords/latin-square","display_name":"Latin square","score":0.671533465385437},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5938323736190796},{"id":"https://openalex.org/keywords/orthogonal-array","display_name":"Orthogonal array","score":0.5735419392585754},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.34355032444000244},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3332618474960327}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8638970851898193},{"id":"https://openalex.org/C158887663","wikidata":"https://www.wikidata.org/wiki/Q679367","display_name":"Latin square","level":4,"score":0.671533465385437},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5938323736190796},{"id":"https://openalex.org/C42632107","wikidata":"https://www.wikidata.org/wiki/Q2031860","display_name":"Orthogonal array","level":3,"score":0.5735419392585754},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.34355032444000244},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3332618474960327},{"id":"https://openalex.org/C100544194","wikidata":"https://www.wikidata.org/wiki/Q41760","display_name":"Fermentation","level":2,"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/C83469408","wikidata":"https://www.wikidata.org/wiki/Q2036525","display_name":"Taguchi methods","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},{"id":"https://openalex.org/C70262065","wikidata":"https://www.wikidata.org/wiki/Q427652","display_name":"Rumen","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10623-025-01629-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01629-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01629-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10623-025-01629-5","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10623-025-01629-5","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10623-025-01629-5.pdf","source":{"id":"https://openalex.org/S81616010","display_name":"Designs Codes and Cryptography","issn_l":"0925-1022","issn":["0925-1022","1573-7586"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Designs, Codes and Cryptography","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320965","display_name":"University of New South Wales","ror":"https://ror.org/03r8z3t63"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4410815247.pdf","grobid_xml":"https://content.openalex.org/works/W4410815247.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1976677460","https://openalex.org/W2004598385","https://openalex.org/W2007600913","https://openalex.org/W2069903885","https://openalex.org/W2148602768","https://openalex.org/W2964326359","https://openalex.org/W4212960282"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2044829724","https://openalex.org/W169006039","https://openalex.org/W2364512413","https://openalex.org/W2042914544","https://openalex.org/W2390590114","https://openalex.org/W4388328977","https://openalex.org/W2376096933","https://openalex.org/W4389478513","https://openalex.org/W2124016695"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2],"paper,":[3],"respectively":[4,39,95],"8,":[5],"10":[6,117],"and":[7,27,35,55,77,100,118,134],"9":[8,34],"mutually":[9],"orthogonal":[10],"Latin":[11],"squares":[12],"(MOLS)":[13],"of":[14,65,121,166],"sizes":[15,122],"$$n=54$$":[16,46],"<mml:math":[17,47,69,81,124,140,169],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[18,48,70,82,125,141,170],"<mml:mrow>":[19,49,71,83,126,142,171],"<mml:mi>n</mml:mi>":[20,50,127,143,172],"<mml:mo>=</mml:mo>":[21,51,128,144,173],"<mml:mn>54</mml:mn>":[22,52,74],"</mml:mrow>":[23,53,75,87,130,146,175],"</mml:math>":[24,54,76,88,131,147,176],",":[25,132],"96":[26,56,99],"108":[28],"are":[29,57],"obtained":[30,58,149],"(previously,":[31],"only":[32],"5,":[33],"8":[36,119],"MOLS":[37,120,165],"were":[38],"known":[40],"for":[41],"these":[42,93],"values).":[43],"The":[44,137],"cases":[45],"by":[59,150],"constructing":[60,151,163],"separable":[61],"permutation":[62],"codes":[63,94],"consisting":[64],"$$8":[66],"\\times":[67,79],"54$$":[68],"<mml:mn>8</mml:mn>":[72],"<mml:mo>\u00d7</mml:mo>":[73,85],"$$10":[78],"96$$":[80],"<mml:mn>10</mml:mn>":[84],"<mml:mn>96</mml:mn>":[86],"codewords,":[89],"respectively;":[90],"in":[91,110],"addition,":[92],"have":[96],"lengths":[97],"54,":[98],"minimum":[101],"distances":[102],"53,":[103],"95.":[104],"This":[105],"construction":[106],"method":[107],"was":[108],"used":[109],"an":[111],"earlier":[112],"paper":[113],"to":[114],"obtain":[115],"6,":[116],"$$n=35$$":[123],"<mml:mn>35</mml:mn>":[129],"54":[133],"63,":[135],"respectively.":[136],"case":[138],"$$n=108$$":[139],"<mml:mn>108</mml:mn>":[145],"is":[148,177],"a":[152,159],"(108,":[153],"10,":[154],"1)":[155],"difference":[156],"matrix.":[157],"Also,":[158],"previous":[160],"error":[161],"when":[162],"6":[164],"size":[167],"$$n=45$$":[168],"<mml:mn>45</mml:mn>":[174],"corrected.":[178]},"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}