{"id":"https://openalex.org/W2798464829","doi":"https://doi.org/10.37236/7827","title":"A New Lower Bound for the Size of an Affine Blocking Set","display_name":"A New Lower Bound for the Size of an Affine Blocking Set","publication_year":2018,"publication_date":"2018-11-30","ids":{"openalex":"https://openalex.org/W2798464829","doi":"https://doi.org/10.37236/7827","mag":"2798464829"},"language":"en","primary_location":{"id":"doi:10.37236/7827","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7827","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p40/pdf","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":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p40/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036668364","display_name":"Maarten De Boeck","orcid":"https://orcid.org/0000-0001-8399-9064"},"institutions":[{"id":"https://openalex.org/I2801227569","display_name":"Ghent University Hospital","ror":"https://ror.org/00xmkp704","country_code":"BE","type":"healthcare","lineage":["https://openalex.org/I2801227569"]},{"id":"https://openalex.org/I32597200","display_name":"Ghent University","ror":"https://ror.org/00cv9y106","country_code":"BE","type":"education","lineage":["https://openalex.org/I32597200"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Maarten De Boeck","raw_affiliation_strings":["Ghent University","#N#Ghent University#N#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ghent University","institution_ids":["https://openalex.org/I2801227569"]},{"raw_affiliation_string":"#N#Ghent University#N#","institution_ids":["https://openalex.org/I32597200"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5036469410","display_name":"Geertrui Van de Voorde","orcid":"https://orcid.org/0000-0002-4957-6911"},"institutions":[{"id":"https://openalex.org/I185492890","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39","country_code":"NZ","type":"education","lineage":["https://openalex.org/I185492890"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Geertrui Van de Voorde","raw_affiliation_strings":["University of Canterbury"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Canterbury","institution_ids":["https://openalex.org/I185492890"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03381527,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"4","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":0.9991000294685364,"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":0.9991000294685364,"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":0.9836000204086304,"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":0.9818999767303467,"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/affine-transformation","display_name":"Affine transformation","score":0.8144918084144592},{"id":"https://openalex.org/keywords/blocking","display_name":"Blocking (statistics)","score":0.7889183163642883},{"id":"https://openalex.org/keywords/affine-plane","display_name":"Affine plane (incidence geometry)","score":0.7578645944595337},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6961443424224854},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6531761884689331},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.6402049660682678},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.6270009279251099},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.613013505935669},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.527413010597229},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.4627843499183655},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44571566581726074},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.38301753997802734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.19968706369400024},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18752002716064453},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15395468473434448},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11551758646965027},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05548340082168579}],"concepts":[{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.8144918084144592},{"id":"https://openalex.org/C144745244","wikidata":"https://www.wikidata.org/wiki/Q4927286","display_name":"Blocking (statistics)","level":2,"score":0.7889183163642883},{"id":"https://openalex.org/C154610627","wikidata":"https://www.wikidata.org/wiki/Q382491","display_name":"Affine plane (incidence geometry)","level":3,"score":0.7578645944595337},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6961443424224854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6531761884689331},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.6402049660682678},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.6270009279251099},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.613013505935669},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.527413010597229},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.4627843499183655},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44571566581726074},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38301753997802734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.19968706369400024},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18752002716064453},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15395468473434448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11551758646965027},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05548340082168579},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.37236/7827","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7827","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p40/pdf","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"},{"id":"pmh:oai:arXiv.org:1804.09511","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1804.09511","pdf_url":"https://arxiv.org/pdf/1804.09511","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},{"id":"mag:2798464829","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1804.09511.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:archive.ugent.be:8590120","is_oa":true,"landing_page_url":"https://biblio.ugent.be/publication/8590120","pdf_url":null,"source":{"id":"https://openalex.org/S4306400478","display_name":"Ghent University Academic Bibliography (Ghent University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I32597200","host_organization_name":"Ghent University","host_organization_lineage":["https://openalex.org/I32597200"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nd","license_id":"https://openalex.org/licenses/cc-by-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 1077-8926","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1804.09511","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1804.09511","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.37236/7827","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7827","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v25i4p40/pdf","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":[{"id":"https://openalex.org/F4320310502","display_name":"University of Canterbury","ror":"https://ror.org/03y7q9t39"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2798464829.pdf","grobid_xml":"https://content.openalex.org/works/W2798464829.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2074530386","https://openalex.org/W2092400881","https://openalex.org/W2092976320","https://openalex.org/W2099471393","https://openalex.org/W2324078777","https://openalex.org/W4237310309"],"related_works":["https://openalex.org/W2964025388","https://openalex.org/W2802332212","https://openalex.org/W2027916974","https://openalex.org/W1999195572","https://openalex.org/W2027429657","https://openalex.org/W2070377429","https://openalex.org/W2281101862","https://openalex.org/W2949153607","https://openalex.org/W2982852936","https://openalex.org/W1510434836","https://openalex.org/W2052031636","https://openalex.org/W2964164680","https://openalex.org/W2573382822","https://openalex.org/W2007217473","https://openalex.org/W3001610491","https://openalex.org/W2740150177","https://openalex.org/W1971483333","https://openalex.org/W3010894784","https://openalex.org/W2573632767","https://openalex.org/W2017218306"],"abstract_inverted_index":{"A":[0],"blocking":[1,30,58],"set":[2,9,59],"in":[3,32,39],"an":[4,61],"affine":[5,35,62],"plane":[6,63],"is":[7],"a":[8,57],"of":[10,22,60,64],"points":[11],"$B$":[12],"such":[13],"that":[14,56],"every":[15],"line":[16],"contains":[17,69],"at":[18,70],"least":[19,71],"one":[20],"point":[21],"$B$.":[23],"The":[24],"best":[25],"known":[26],"lower":[27],"bound":[28],"for":[29],"sets":[31],"arbitrary":[33],"(non-desarguesian)":[34],"planes":[36],"was":[37],"derived":[38],"the":[40],"1980's":[41],"by":[42,54],"Bruen":[43],"and":[44],"Silverman.":[45],"In":[46],"this":[47,52],"note,":[48],"we":[49],"improve":[50],"on":[51],"result":[53],"showing":[55],"order":[65],"$q$,":[66],"$q\\geqslant":[67],"25$,":[68],"$q+\\lfloor\\sqrt{q}\\rfloor+3$":[72],"points.":[73]},"counts_by_year":[],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}