{"id":424,"date":"2021-07-26T13:57:08","date_gmt":"2021-07-26T13:57:08","guid":{"rendered":"https:\/\/site.uvm.edu\/jdinitz\/?page_id=424"},"modified":"2021-07-26T15:57:38","modified_gmt":"2021-07-26T15:57:38","slug":"new-results-in-part-vii","status":"publish","type":"page","link":"https:\/\/site.uvm.edu\/jdinitz\/?page_id=424","title":{"rendered":"New Results in Part VII"},"content":{"rendered":"\n<p>   <\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"53\" src=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/05\/image-6.png\" alt=\"\" class=\"wp-image-431\" \/><\/figure>\n\n\n\n<p>This page contains new results in the area of combinatorial designs that have occurred since the publication of the <em>Handbook of Combinatorial Designs, Second Edition <\/em>in November 2006. The results here would be contained in Part VII of the Handbook.<\/p>\n\n\n\n<p>Last edited 10\/19\/2018<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/07\/rutbar.gif\" alt=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/07\/rutbar.gif\" \/><\/figure>\n\n\n\n<p>Page 714, Table 2.110: The lower bound for r = 9, q = 16 has been improved from 128 to 129 by Axel Konert. Also, Simeon Ball is maintaining an online version of this table at <a href=\"http:\/\/www-ma4.upc.es\/~simeon\/codebounds.html\">http:\/\/www-ma4.upc.es\/~simeon\/codebounds.html<\/a>. Axel Kohnert (Axel.Kohnert@uni-bayreuth.de) Nov. 2006.<\/p>\n\n\n\n<p>Page 743, Table 5.26: LF(14) = 98758655816833727741338583040. This was computed by Patric Ostergard and Petteri Kaski. Petteri Kaski (petteri.kaski@cs.helsinki.fi), Sept. 2007. They also proved that NF(14) = 1132835421602062347. A preprint is available at <a href=\"http:\/\/arxiv.org\/abs\/0801.0202\">http:\/\/arxiv.org\/abs\/0801.0202<\/a>. Petteri Kaski (petteri.kaski@cs.helsinki.fi), Jan. 2008.<\/p>\n\n\n\n<p>Page 752, Theorem 5.62: New perfect 1-factorizations have been found for the following orders: 2476100, 2685620, 3442952, 4657464, 5735340, 6436344, 1030302, 2048384, 4330748, 6967872, 7880600, 9393932, 11089568, 11697084, 13651920, 15813252, 18191448, 19902512, 22665188. Also, Ian Wanless is keeping a list of P1F&#8217;s at <a href=\"http:\/\/www.maths.monash.edu.au\/~iwanless\/data\/P1F\/newP1F.html\">http:\/\/www.maths.monash.edu.au\/~iwanless\/data\/P1F\/newP1F.html<\/a>. Ian Wanless (Ian.Wanless@sci.monash.edu.au) March 2007.<\/p>\n\n\n\n<p>Page 752, Theorem 5.62: A perfect 1-factorizations was found for K<sub>52<\/sub> (Adam Wolfe, <em>JCD<\/em> <strong>17<\/strong>, 2009, pp 190 &#8212; 196)&nbsp; and <a href=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/05\/perfect.k56.pdf\" data-type=\"URL\" data-id=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/05\/perfect.k56.pdf\">a perfect 1-factorizations was found for K<sub>56<\/sub><\/a> by David Pike (dapike@mun.ca) Oct. 2018.<\/p>\n\n\n\n<p>Page 754. Section 5.8: It has been shown that the 2-transitive 2-factorizations of K<sub>v<\/sub> are precisely those in which v = p<sup>n<\/sup> with p a prime and each 2-factor is the union of p-cycles obtainable from a parallel class of lines of AG(n, p) in a suitable manner. The reference is A. Bonisoli, M. Buratti and G. Mazzuoccolo, Doubly transitive 2-factorizations, <em>J. Combin. Des<\/em>.<strong> 15<\/strong> (2007), 120-132. Marco Buratti (buratti@dmi.unipg.it), June 2012.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/07\/rutbar.gif\" alt=\"https:\/\/site.uvm.edu\/jdinitz\/files\/2021\/07\/rutbar.gif\" \/><\/figure>\n\n\n\n<p>Return to the <a href=\"https:\/\/site.uvm.edu\/jdinitz\/?page_id=373&amp;preview=true\" data-type=\"URL\" data-id=\"https:\/\/site.uvm.edu\/jdinitz\/?page_id=373&amp;preview=true\">HCD new results home page.<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This page contains new results in the area of combinatorial designs that have occurred since the publication of the Handbook of Combinatorial Designs, Second Edition in November 2006. The results here would be contained in Part VII of the Handbook. Last edited 10\/19\/2018 Page 714, Table 2.110: The lower bound for r = 9, q &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/site.uvm.edu\/jdinitz\/?page_id=424\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;New Results in Part VII&#8221;<\/span><\/a><\/p>\n","protected":false},"author":6743,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-424","page","type-page","status-publish","hentry","entry"],"featured_image_src":null,"featured_image_src_square":null,"_links":{"self":[{"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=\/wp\/v2\/pages\/424","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=\/wp\/v2\/users\/6743"}],"replies":[{"embeddable":true,"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=424"}],"version-history":[{"count":9,"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=\/wp\/v2\/pages\/424\/revisions"}],"predecessor-version":[{"id":476,"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=\/wp\/v2\/pages\/424\/revisions\/476"}],"wp:attachment":[{"href":"https:\/\/site.uvm.edu\/jdinitz\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=424"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}