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 368, Theorem 11.29. (44,5, λ) coverings are now known for λ = 17 and λ ≡ 13 (mod 20). Julian Abel (r.j.abel@unsw.edu.au). 8/09

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 575, Remark 46.6 and Theorem 46.7: Colbourn [529] developed a strategy for group testing when the clones are linearly ordered and the positive clones form a consecutive subset of the set of all clones. Jimbo and his collaborators improved Colbourn's strategy by considering the error detecting and correcting capability of group testing. In order to correct false negative or false positive clones in the pool outcomes, Momihara and Jimbo suggest the investigation of block sequences of maximum packings MP(t,k,v) which contains the blocks exactly once such that the collection of all blocks together with all unions of two consecutive blocks of this sequence forms an error correcting code with minimum distance d. Such a sequence is usually called a block sequence with consecutive unions having minimum distance d, and denoted by BSCU(t,k,v|d). Ge, Miao and Zhang ("On block sequences of Steiner quadruple systems with error correcting consecutive unions", SIAM J. Discrete Math., to appear) showed that the necessary conditions for the existence of BSCU(3,4,v|4)'s of Steiner quadruple systems, namely, v ≡ 2,4 mod(6) and v ≥ 4, are also sufficient except for v = 8,10.
Some small useful cyclic sequence of blocks with consecutive unions can be found here. This is essentially the appendix to the paper by Ge, Miao and Zhang mentioned above. Ying Miao (miao@sk.tsukuba.ac.jp), 3/09

Page 624, Table 55.30. DS(35) = 2138089212789. (V. Linja-aho and P. R. J. Ostergard, "Classification of starters" to appear in Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC). Vesa Linja-aho (vesa.linja-aho@tkk.fi), 5/09

Page 625, Table 55.36. There are corrections to several values in this table. They are:
There are 2 distinct strong starters for n=7 (not 1).
There are 8 distinct strong starters for n=13 (not 4).
There are 6660 distinct strong starters for n=21 (not 6600).
There are 1201626 distinct strong starters for n=27 (not 1249650).
There are 66757 inequivalent strong starters for n=27 (not 69425).
In addition, the number of strong starters in cyclic groups has been computed up to n = 37. All of this can be found V. Linja-aho and P. R. J. Ostergard, "Classification of starters" to appear in Journal of Combinatorial Mathematics and Combinatorial Computing (JCMCC). Vesa Linja-aho (vesa.linja-aho@tkk.fi), 5/09

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

Page 660, Theorem 63.33 and Remark 63.34: In 1987, Hartman showed that the necessary condition v ≡ 4 or 8 (mod 12) for the existence of a resolvable SQS(v) is also sufficient for all values of v, with 23 possible exceptions. These last 23 undecided orders were removed by Ji and Zhu in 2005, where the concept of resolvable H-designs was introduced to construct resolvable SQSs.

Zhang and Ge ("Existence of resolvable H-designs with group sizes 2,3,4 and 6", Designs, Codes and Cryptography, to appear) showed that: The necessary conditions gn ≡ 0 (mod 4), g(n-1)(n-2) ≡ 0 (mod 3) and n ≥ 4 for the existence of a resolvable H-design of type g^{n} are also sufficient for each g = 1,2,3,5,6,7,9,10,11 (mod 12), and also sufficient for each g ≡ 4,8 (mod 12) with two possible exceptions n=73,149. Direct constructions for RH(4¹⁹) and RH(4⁴¹) can be found here. This is essentially the appendix to the paper by Zhang and Ge mentioned above. As a consequence, they also show that the necessary conditions for the existence of a resolvable G-design of type g^n are also sufficient. Xiande Zhang (xdzhangzju@163.com). 9/09

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