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 VI of the Handbook.
Last edited 6/8/08
Page 346, Conjecture 6.8: The Hall-Paige conjecture has been proved. J. N. Bray, A. B. Evans (anthony.evans@wright.edu), and S. Wilcox (swilcox@fas.harvard.edu ). 2/08
Page 360, Table 9.36: The enumeration of Costas Arrays of orders 27 is complete. C(27)=204 and c(27)=29. Also, there is now an excellent website devoted to information concerning Costas Arrays, the URL is http://www.costasarrays.org/ . Scott Rickard (scott.rickard@ucd.ie). 5/08
Page 397, Theorem 16.29: The bound that q > {k \choose 2}^{k(k-1)} can be improved to q > ({k \choose 2}^{2k})/ \gcd({k \choose 2},\lambda)^{2k-2}). Anita Pasotti (anita.pasotti@ing.unibs.it). 4/08
Page 417, Theorem 17.52: V(9,t) vectors exist for all for t > 8, q = 9t+1 a prime power, except possibly for q = 56. (K. Chen, Z. Cao and R. Wei, Existence of V(9,t) vectors, JCMCC 55 (2005), 209-221).
Page 478, near Theorem 24.10: If G is a simple graph with e edges and degeneracy d (that is the largest minimal degree among the minimal degrees of all the subgraphs of G), then there exists an elementary abelian (K_q,G)-design for every prime power q such that e^{2d+2} < q \equiv 1 (mod 2e). Anita Pasotti (anita.pasotti@ing.unibs.it). 4/08
Page 569, Theorem 44.4: In addition, M(n,d) is not equal to n!/(d-1)!-1. (J. Quistorff, Electron. J. Combin., 13 (2006), #A1, www.combinatorics.org/Volume_13/PDF/v13i1a1.pdf). Peter Dukes (dukes@uvic.ca), 11/07
Page 634, Theorem 57.11: Super-simple (v,5,2) BIBDs exist for v = 115 and 135 (R.J.R. Abel and F.E. Bennett, Discrete Appl. Math. 156 (2008), 780-793. Julian Abel (rjabel@unsw.edu.au), 3/08
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