{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T18:58:39Z","timestamp":1775329119247,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[2018,12,21]],"date-time":"2018-12-21T00:00:00Z","timestamp":1545350400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000838","name":"University of Sussex","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100000838","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s10623-018-00592-8","type":"journal-article","created":{"date-parts":[[2018,12,21]],"date-time":"2018-12-21T02:54:41Z","timestamp":1545360881000},"page":"679-683","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A new lower bound for the smallest complete (k,\u00a0n)-arc in $$\\mathrm {PG}(2,q)$$ PG ( 2 , q )"],"prefix":"10.1007","volume":"87","author":[{"given":"S.","family":"Alabdullah","sequence":"first","affiliation":[]},{"given":"J. W. P.","family":"Hirschfeld","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,21]]},"reference":[{"key":"592_CR1","unstructured":"Bartoli D., Marcugini S., Pambianco F.: The maximum and the minimum sizes of complete $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,16)$$ P G ( 2 , 16 ) . In: Thirteenth International Workshop on Algebraic and Combinatorial Coding Theory, Pomorie, Bulgaria, pp. 77\u201382, 15\u201321 June 2012."},{"key":"592_CR2","doi-asserted-by":"publisher","first-page":"487","DOI":"10.1007\/s10623-015-0073-7","volume":"79","author":"D Bartoli","year":"2015","unstructured":"Bartoli D., Giulietti M., Zini G.: Complete $$(k,3)$$ ( k , 3 ) -arcs from quartic curves. Des. Codes Cryptogr. 79, 487\u2013505 (2015).","journal-title":"Des. Codes Cryptogr."},{"key":"592_CR3","first-page":"145","volume":"45","author":"J Bierbrauer","year":"2003","unstructured":"Bierbrauer J.: The maximal size of a 3-arc in $$\\text{ PG }(2,8)$$ PG ( 2 , 8 ) . J. Comb. Math. Comb. Comput. 45, 145\u2013161 (2003).","journal-title":"J. Comb. Math. Comb. Comput."},{"key":"592_CR4","doi-asserted-by":"publisher","first-page":"459","DOI":"10.1002\/jcd.20211","volume":"17","author":"K Coolsaet","year":"2009","unstructured":"Coolsaet K., Sticker H.: A full classification of the complete $$k$$ k -arcs in $$PG(2,23)$$ P G ( 2 , 23 ) and $$PG(2,25)$$ P G ( 2 , 25 ) . J. Comb. Des. 17, 459\u2013477 (2009).","journal-title":"J. Comb. Des."},{"key":"592_CR5","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1002\/jcd.20261","volume":"19","author":"K Coolsaet","year":"2011","unstructured":"Coolsaet K., Sticker H.: The complete $$k$$ k -arcs of $${\\rm PG}(2,27)$$ PG ( 2 , 27 ) and $${\\rm PG}(2,29)$$ PG ( 2 , 29 ) . J. Comb. Des. 19, 111\u2013130 (2011).","journal-title":"J. Comb. Des."},{"key":"592_CR6","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1002\/jcd.20293","volume":"20","author":"K Coolsaet","year":"2012","unstructured":"Coolsaet K., Sticker H.: The complete $$(k,3)$$ ( k , 3 ) -arcs of $$\\text{ PG }(2, q), q\\le 13$$ PG ( 2 , q ) , q \u2264 13 . J. Comb. Des. 20, 89\u2013111 (2012).","journal-title":"J. Comb. Des."},{"key":"592_CR7","unstructured":"Hirschfeld J.W.P.: Projective Geometries Over Finite Fields, pp. xii+474. Clarendon Press, Oxford (1979)."},{"key":"592_CR8","doi-asserted-by":"crossref","unstructured":"Hirschfeld J.W.P.: Projective Geometries Over Finite Fields, 2nd edn, pp. xiv+555. Oxford University Press, Oxford (1998).","DOI":"10.1093\/oso\/9780198502951.001.0001"},{"key":"592_CR9","doi-asserted-by":"publisher","first-page":"184","DOI":"10.1002\/jcd.21426","volume":"24","author":"JWP Hirschfeld","year":"2016","unstructured":"Hirschfeld J.W.P., Pichanick E.V.D.: Bounds for arcs of arbitrary degree in finite Desargusian planes. J. Comb. Des. 24, 184\u2013196 (2016).","journal-title":"J. Comb. Des."},{"key":"592_CR10","unstructured":"Marcugini S., Milani A., Pambianco F.: A computer based classification of the $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,7)$$ P G ( 2 , 7 ) . Rapporto Tecnico n.7 (1998)."},{"key":"592_CR11","unstructured":"Marcugini S., Milani A., Pambianco F.: A computer based classification of the $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,8)$$ P G ( 2 , 8 ) . Rapporto Tecnico n.8 (1998)."},{"key":"592_CR12","unstructured":"Marcugini S., Milani A., Pambianco F.: A computer based classification of the $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,9)$$ P G ( 2 , 9 ) . Rapporto Tecnico n.9 (1998)."},{"issue":"209","key":"592_CR13","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1016\/S0012-365X(99)00202-2","volume":"208","author":"S Marcugini","year":"1999","unstructured":"Marcugini S., Milani A., Pambianco F.: Maximal $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,11)$$ P G ( 2 , 11 ) . Discret. Math. 208(209), 421\u2013426 (1999).","journal-title":"Discret. Math."},{"key":"592_CR14","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1016\/j.disc.2004.04.043","volume":"294","author":"S Marcugini","year":"2005","unstructured":"Marcugini S., Milani A., Pambianco F.: Maximal $$(n,3)$$ ( n , 3 ) -arcs in $$PG(2,13)$$ P G ( 2 , 13 ) . Discret. Math. 294, 139\u2013145 (2005).","journal-title":"Discret. Math."},{"key":"592_CR15","doi-asserted-by":"publisher","first-page":"739","DOI":"10.1016\/j.disc.2005.11.094","volume":"307","author":"S Marcugini","year":"2007","unstructured":"Marcugini S., Milani A., Pambianco F.: Complete arcs in $$PG(2,25)$$ P G ( 2 , 25 ) : the spectrum of size and the classification of the smallest complete arcs. Discret. Math. 307, 739\u2013747 (2007).","journal-title":"Discret. Math."}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10623-018-00592-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-018-00592-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-018-00592-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,4]],"date-time":"2026-04-04T18:20:16Z","timestamp":1775326816000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10623-018-00592-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,21]]},"references-count":15,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["592"],"URL":"https:\/\/doi.org\/10.1007\/s10623-018-00592-8","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"value":"0925-1022","type":"print"},{"value":"1573-7586","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,12,21]]},"assertion":[{"value":"10 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 December 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}