Handbook of Combinatorial Designs, Second Edition

New Results in Part VII

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 7/5/08

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 http://www-ma4.upc.es/~simeon/codebounds.html. Axel Kohnert (Axel.Kohnert@uni-bayreuth.de) Nov. 2006.

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 http://arxiv.org/abs/0801.0202. Petteri Kaski (petteri.kaski@cs.helsinki.fi), Jan. 2008.

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's at http://www.maths.monash.edu.au/~iwanless/data/P1F/newP1F.html. Ian Wanless (Ian.Wanless@sci.monash.edu.au) March 2007.

Page 754. Section 5.8: It has been shown that the 2-transitive 2-factorizations of Kv are precisely those in which v = pn 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, J. Combin. Des. 15 (2007), 120-132. Marco Buratti (buratti@dmi.unipg.it), June 2012.

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