{"id":"https://openalex.org/W4396651053","doi":"https://doi.org/10.22331/q-2026-02-23-2008","title":"Generalized group designs: constructing novel unitary 2-, 3- and 4-designs","display_name":"Generalized group designs: constructing novel unitary 2-, 3- and 4-designs","publication_year":2026,"publication_date":"2026-02-23","ids":{"openalex":"https://openalex.org/W4396651053","doi":"https://doi.org/10.22331/q-2026-02-23-2008"},"language":"en","primary_location":{"id":"doi:10.22331/q-2026-02-23-2008","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-02-23-2008","pdf_url":"https://quantum-journal.org/papers/q-2026-02-23-2008/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://quantum-journal.org/papers/q-2026-02-23-2008/pdf/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5035760347","display_name":"\u00c1goston Kaposi","orcid":"https://orcid.org/0009-0007-7604-1449"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I4210126225","display_name":"HUN-REN Wigner Research Centre for Physics","ror":"https://ror.org/035dsb084","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210126225","https://openalex.org/I4387152226"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"\u00c1goston Kaposi","raw_affiliation_strings":["Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/C, Budapest, H-1117, Hungary","Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/C, Budapest, H-1117, Hungary","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary","institution_ids":["https://openalex.org/I4210126225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045203400","display_name":"Zolt\u00e1n Kolarovszki","orcid":"https://orcid.org/0009-0001-9837-5534"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I4210126225","display_name":"HUN-REN Wigner Research Centre for Physics","ror":"https://ror.org/035dsb084","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210126225","https://openalex.org/I4387152226"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n Kolarovszki","raw_affiliation_strings":["Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/C, Budapest, H-1117, Hungary","Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/C, Budapest, H-1117, Hungary","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary","institution_ids":["https://openalex.org/I4210126225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043448989","display_name":"Adrian Solymos","orcid":"https://orcid.org/0009-0008-5734-4871"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I4210126225","display_name":"HUN-REN Wigner Research Centre for Physics","ror":"https://ror.org/035dsb084","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210126225","https://openalex.org/I4387152226"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Adrian Solymos","raw_affiliation_strings":["Department of Physics of Complex Systems, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/A, Budapest, H-1117, Hungary","Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics of Complex Systems, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/A, Budapest, H-1117, Hungary","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary","institution_ids":["https://openalex.org/I4210126225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018285963","display_name":"Zolt\u00e1n Zimbor\u00e1s","orcid":"https://orcid.org/0000-0002-2184-526X"},"institutions":[{"id":"https://openalex.org/I106118109","display_name":"E\u00f6tv\u00f6s Lor\u00e1nd University","ror":"https://ror.org/01jsq2704","country_code":"HU","type":"education","lineage":["https://openalex.org/I106118109"]},{"id":"https://openalex.org/I133731052","display_name":"University of Helsinki","ror":"https://ror.org/040af2s02","country_code":"FI","type":"education","lineage":["https://openalex.org/I133731052"]},{"id":"https://openalex.org/I4210126225","display_name":"HUN-REN Wigner Research Centre for Physics","ror":"https://ror.org/035dsb084","country_code":"HU","type":"facility","lineage":["https://openalex.org/I4210126225","https://openalex.org/I4387152226"]}],"countries":["FI","HU"],"is_corresponding":false,"raw_author_name":"Zolt\u00e1n Zimbor\u00e1s","raw_affiliation_strings":["Algorithmiq Ltd, Kanavakatu 3C, Helsinki, 00160, Finland","Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/C, Budapest, H-1117, Hungary","Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary","University of Helsinki, Yliopistonkatu 4, Helsinki, 00100, Finland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Algorithmiq Ltd, Kanavakatu 3C, Helsinki, 00160, Finland","institution_ids":[]},{"raw_affiliation_string":"Department of Programming Languages and Compilers, E\u00f6tv\u00f6s Lor\u00e1nd University, P\u00e1zm\u00e1ny P\u00e9ter s\u00e9t\u00e1ny 1/C, Budapest, H-1117, Hungary","institution_ids":["https://openalex.org/I106118109"]},{"raw_affiliation_string":"Quantum Computing and Quantum Information Research Group, HUN-REN Wigner Research Centre for Physics, Konkoly\u2013Thege Mikl\u00f3s \u00fat 29-33, Budapest, H-1525, Hungary","institution_ids":["https://openalex.org/I4210126225"]},{"raw_affiliation_string":"University of Helsinki, Yliopistonkatu 4, Helsinki, 00100, Finland","institution_ids":["https://openalex.org/I133731052"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":200,"currency":"EUR","value_usd":215},"apc_paid":{"value":200,"currency":"EUR","value_usd":215},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00053715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":null,"first_page":"2008","last_page":"2008"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9771000146865845,"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":0.9771000146865845,"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/T11798","display_name":"Optimal Experimental Design Methods","score":0.9521999955177307,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/unitary-state","display_name":"Unitary state","score":0.7700862884521484},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.6393576860427856},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.5105205774307251},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49919748306274414},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4715186357498169},{"id":"https://openalex.org/keywords/unitary-group","display_name":"Unitary group","score":0.45549261569976807},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.171377032995224},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.11960136890411377}],"concepts":[{"id":"https://openalex.org/C67820243","wikidata":"https://www.wikidata.org/wiki/Q179164","display_name":"Unitary state","level":2,"score":0.7700862884521484},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.6393576860427856},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.5105205774307251},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49919748306274414},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4715186357498169},{"id":"https://openalex.org/C99072794","wikidata":"https://www.wikidata.org/wiki/Q1500617","display_name":"Unitary group","level":3,"score":0.45549261569976807},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.171377032995224},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.11960136890411377},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.22331/q-2026-02-23-2008","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-02-23-2008","pdf_url":"https://quantum-journal.org/papers/q-2026-02-23-2008/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2405.00919","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2405.00919","pdf_url":"https://arxiv.org/pdf/2405.00919","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:doi:10.48550/arxiv.2405.00919","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"pmh:oai:doaj.org/article:ff540a5e8dea40dda62e5a5c5971329f","is_oa":true,"landing_page_url":"https://doaj.org/article/ff540a5e8dea40dda62e5a5c5971329f","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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Quantum, Vol 10, p 2008 (2026)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2405.00919","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2405.00919","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.22331/q-2026-02-23-2008","is_oa":true,"landing_page_url":"https://doi.org/10.22331/q-2026-02-23-2008","pdf_url":"https://quantum-journal.org/papers/q-2026-02-23-2008/pdf/","source":{"id":"https://openalex.org/S4210226432","display_name":"Quantum","issn_l":"2521-327X","issn":["2521-327X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317900","host_organization_name":"Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften","host_organization_lineage":["https://openalex.org/P4310317900"],"host_organization_lineage_names":["Verein zur F\u00f6rderung des Open Access Publizierens in den Quantenwissenschaften"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Quantum","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2511972022","display_name":null,"funder_award_id":"101113946 OpenSuperQPlus100","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"},{"id":"https://openalex.org/G3731544974","display_name":null,"funder_award_id":"101113946","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"},{"id":"https://openalex.org/G4308803315","display_name":null,"funder_award_id":"2022-2.1.1-NL-2022-00004","funder_id":"https://openalex.org/F4320336675","funder_display_name":"National Research, Development and Innovation Office"},{"id":"https://openalex.org/G453600707","display_name":null,"funder_award_id":"HQCC-101017733","funder_id":"https://openalex.org/F4320330828","funder_display_name":"QuantERA"},{"id":"https://openalex.org/G5363030257","display_name":null,"funder_award_id":"2022-2.1.1-NL-2022-00004","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G5442384851","display_name":null,"funder_award_id":"HORIZON-CL4-2022-QUANTUM-01-SGA","funder_id":"https://openalex.org/F4320334322","funder_display_name":"HORIZON EUROPE Framework Programme"},{"id":"https://openalex.org/G5670265214","display_name":null,"funder_award_id":"FK135220","funder_id":"https://openalex.org/F4320326762","funder_display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal"},{"id":"https://openalex.org/G575169067","display_name":null,"funder_award_id":"101017733","funder_id":"https://openalex.org/F4320330828","funder_display_name":"QuantERA"}],"funders":[{"id":"https://openalex.org/F4320326762","display_name":"Nemzeti Kutat\u00e1si Fejleszt\u00e9si \u00e9s Innov\u00e1ci\u00f3s Hivatal","ror":null},{"id":"https://openalex.org/F4320330828","display_name":"QuantERA","ror":null},{"id":"https://openalex.org/F4320334322","display_name":"HORIZON EUROPE Framework Programme","ror":null},{"id":"https://openalex.org/F4320336675","display_name":"National Research, Development and Innovation Office","ror":null},{"id":"https://openalex.org/F4320338388","display_name":"Eurostars","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4396651053.pdf","grobid_xml":"https://content.openalex.org/works/W4396651053.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1848366941","https://openalex.org/W2085208370","https://openalex.org/W2071880083","https://openalex.org/W2045516162","https://openalex.org/W2790056202","https://openalex.org/W2537703961","https://openalex.org/W3131645664","https://openalex.org/W2019630194","https://openalex.org/W2989593155","https://openalex.org/W3006823398","https://openalex.org/W3099477842","https://openalex.org/W4386734525","https://openalex.org/W4389783226","https://openalex.org/W2140622323","https://openalex.org/W2156626033","https://openalex.org/W2963319228","https://openalex.org/W2192515608","https://openalex.org/W2990431562","https://openalex.org/W2290336547","https://openalex.org/W3213277701","https://openalex.org/W4295004915","https://openalex.org/W1989397443","https://openalex.org/W4249726483","https://openalex.org/W3088477423","https://openalex.org/W4251659063","https://openalex.org/W4382407791","https://openalex.org/W4400710856","https://openalex.org/W2088174526","https://openalex.org/W4411983890","https://openalex.org/W2784023939","https://openalex.org/W3175739012","https://openalex.org/W1515431404","https://openalex.org/W1502291261","https://openalex.org/W4243835777"],"related_works":["https://openalex.org/W2895166062","https://openalex.org/W1651768632","https://openalex.org/W2064597394","https://openalex.org/W4297792916","https://openalex.org/W165541775","https://openalex.org/W3175338421","https://openalex.org/W4299554726","https://openalex.org/W4301308572","https://openalex.org/W2064879546","https://openalex.org/W2023081713"],"abstract_inverted_index":{"Unitary":[0],"designs":[1,16,81,128],"are":[2,17],"essential":[3],"tools":[4],"in":[5,27,112,168],"several":[6],"quantum":[7],"information":[8],"protocols.":[9],"Similarly":[10],"to":[11,20],"other":[12],"design":[13,88],"concepts,":[14],"unitary":[15,31,53,136,151],"mainly":[18],"used":[19],"facilitate":[21],"averaging":[22],"over":[23],"a":[24,90,155],"relevant":[25],"space,":[26],"this":[28,116],"case,":[29],"the":[30,74,84,87,131,135,144],"group":[32,80,103,127,137,152,162],"<mml:math":[33,54,63,69,96,104,145,163],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[34,55,64,70,97,105,146,164],"<mml:mrow":[35],"class=\"MJX-TeXAtom-ORD\">":[36],"<mml:mi":[37],"mathvariant=\"normal\">U</mml:mi>":[38],"</mml:mrow>":[39],"<mml:mo":[40,43],"stretchy=\"false\">(</mml:mo>":[41],"<mml:mi>d</mml:mi>":[42,71],"stretchy=\"false\">)</mml:mo>":[44],"</mml:math>":[45,57,66,72,99,107,148,166],".":[46],"While":[47],"it":[48],"is":[49,157],"known":[50],"that":[51,142],"exact":[52,125],"<mml:mi>t</mml:mi>":[56,65],"-designs":[58,108,167],"exist":[59,110],"for":[60,123,159],"any":[61],"degree":[62],"and":[67,138],"dimension":[68],",":[73],"most":[75,95],"appealing":[76],"type":[77],"of":[78,86,134,150],"designs,":[79],"(in":[82],"which":[83],"elements":[85],"form":[89],"group),":[91],"can":[92,109],"provide":[93],"at":[94],"<mml:mn>3</mml:mn>":[98],"-designs.":[100],"Moreover,":[101],"even":[102],"<mml:mn>2</mml:mn>":[106,165],"only":[111],"limited":[113],"dimensions.":[114,170],"In":[115],"paper,":[117],"we":[118],"present":[119],"novel":[120],"construction":[121,156],"methods":[122],"creating":[124,160],"generalized":[126,161],"based":[129],"on":[130],"representation":[132],"theory":[133],"its":[139],"finite":[140],"subgroups":[141],"overcome":[143],"<mml:mn>4</mml:mn>":[147],"-design-barrier":[149],"designs.":[153],"Furthermore,":[154],"presented":[158],"arbitrary":[169]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2024-05-05T00:00:00"}