# Handbook of Combinatorial Designs, Second Edition

## Errata List

We will be working on this errata list on an ongoing basis. Please send us e-mail concerning any errors that you find in the book so that we can add them to this list.

Thanks to everyone who has pointed out errors, including Julian Abel, Juergen Bierbrauer, Darryn Bryant, Marco Buratti, Yeow Meng Chee, Emily DeWitt, Peter Dukes, Dragomir Djokovic, Daniel Horsley, Jared Howell, Jan de Heer, Saad El-Zanati, Fei Gao, Jianmin Ma, Ebad Mahmoodian, Bill Martin, Ying Miao, Akihiro Munemasa, Patric Östergård, Marco Pavone, David Pike, Joern Quistorff, Giorgio Ragusa, Alex Rosa, Anne Street, Thann Ward, Walter Wlodarski and Victor Zinoviev.

Page 37, line 3: The construction of a BIBD(28,63,9,4,1) is given in IV.1.8 (not in III.1.8).

Page 67, Example 2.67: The solutions to the Kirkman Schoolgirl Problem that are numbered 15a and 15b should be 19a and 19b, respectively.

Page 39, Theorem 2.100: The size of the largest possible independent set is as given. There will be many (most) triple systems where the independent set will be much smaller than those bounds presented. Conversely -- there is at least one example of a triple system with an independent set of the size given for each possible order.

Page 74, Remark 3.15: (42,10,3) should be (40,10,3).

Page 80, Definition 4.9: Insert λ just after the equals sign at the end of the first line. Of course, each λs depends on λ as well as on t, v, and k.

Page 116, Family 6: In item (iii), it should be "t is an odd square", and not "n is an odd square". The reference is number 1660 in the bibliography.

Page 127, Table 7.38: 130 should be 135.

Page 169, Theorem 3.65: In the matrix A2, in row 6 and column 4 the "210", should be "201".

Page 194, Example 4.4: The array given in this example is wrong (apparently also wrong in the first edition). A correct array is here.

Page 252, Table 3.23: The first half of line -3 on page 252, that is, "(247-249) (250-287) (290-295) (290-295)", should just read "(247-287) (290-295)"

Page 254, Table 3.24: 10 should not be in the exception list for Q{01 mod 8} .

Page 254, Theorem 3.25: Q015 mod 8 should be the set of prime powers both >= 8 and \equiv 0,1, or 5 (mod 8).

Page 254, Table 3.26: In entry H{01(4)} \ {4,5}, '(8-61)' should read '(8-56) 60 61'.

Page 256, Theorem 4.6: In condition (1) the 3 should be a 4. Also, in condition (2) the (mod 4) should be (mod 3).

Page 268, Example 6.28: On the 4th line SQS(13) is incorrect, it should be S(2,4,13). On the 5th line SQS(40) is incorrect, it should be S(2,4,40).

Page 270, Table 6.33, line -2: The value of 193 is known; it is given in table VI.7.16 on page 354.

Page 273, Definition 1.5: A Hadamard 3-design has parameters 3-(4n, 2n, n-1).

Page 277, Table 1.50: The numbers 151 and 155 are listed twice. The numbers 71, 131, 165, and 213 should be added to the table.

Page 277, Table 1.51: The second item 63(3) should be replaced by 69(3).

Page 297, Theorem 3.18: 170 should be added to Theorem 3.18.

Page 310, Example 6.43: The BGW(19,9,4; Z2) given in this example is missing a row. The missing row is (0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0).

Page 317, Definition 7.42: Obviously, all the phaseshifts τ should be greater than zero in the definition of Barker sequences. So the correction should read: ... autocorrelation values ρs(τ) satisfy |ρs(τ) | ≤ 1 for all τ , 1 ≤ τ ≤ n-1.

Page 368, Theorem 11.29: v \in {9,13,15,53,63,73,83} should be v \in {9,13,15} and possibly for v \in {53,63,73,83}. (See the newresults page for the case of v=44.)

Page 400, Definition 16.37: In line 3, the expression 1 ≤ m < n ≤ k should be 1 ≤ n < m ≤ k. Also in line 4, the parentheses around quasi-perfect should be deleted.

Page 404, Theorem 16.68: In the 5th statement, "congruent to 1 (mod 12)" should be "congruent to 13 (mod 24)".

Page 405, Remark 16.69: The last sentence should begin: Other base blocks are obtained by multiplying B by (1, ymn) for y a primitive element in GF(q), m = (k-1) / (2 λ) and n = ...

Page 405, Examples 16.70: The block for (v,k, λ) = (91,7,1) should be B = {(0,0), (1,1), (1,12), (2,3), (2,10), (4,4), (4,9)}.

Page 417, Theorem 17.52 (1.): The list of possible exceptions should read "except possibly when (m,t) \in {(8,91), (8,7381)}".

Page 421, Example 18.17: The last entry in the difference set D' for the nonabelian group G should be a5b2 and not a5b.

Page 436 and 437, Proposition 19.9 and Example 19.10: "Golomb ruler" should be "optimal Golomb ruler".

Page 485, Theorem 24.81: The third graph in the list was meant to be K7-S6 (which does not have a ρ-labeling). The graph K7-S5 admits a ρ-labeling.

Page 499, Theorem 29.5: This should read as follows: Let s and n be positive integers with ns2n-1. Then there exists an H(s,2n) ...

Page 527, Example 34.22: In row 5 of the square on the right, the 44 should be a 29 and the 45 should be a 28.

Page 533, Example 35.47: In design number 3, the block (3,6,4) should be (2,6,4).

Page 551, Theorem 40.9: Dλ (v,k,t) should just be D(v,k,t) in both places. Also there should be an additional hypothesis -- namely that k2 > v (t - 1).

Page 583, Remarks 49.6(2) At the end of the third line there should be a right parenthesis.

Page 588, Theorem 50.34.1(iv) This should be t(u-1) is odd.

Page 602, Example 51.84 The foursome in top row of the seventh round is incorrect. 47E0 should be 4TE0.

Page 604, Example 51.95:. This should have stated that 32 teams qualify for the tournament and they are divided into 8 groups of 4 teams each for first round play. The last time that there were only 24 teams was in 1994.

Page 644, Theorem 60.14: The theorem applies to T(t,k,v) rather than T(2,k,v). The references should be to E. S. Mahmoodian and Nasrin Soltankhah, On the existence of (v,k,t)-trades. Australas. J. Combin. 6 (1992), 279--291; and Nasrin Soltankhah, Investigation of existence and non-existence of some (v,k,t)-trades. M.S. thesis, Sharif University of Technology (September 1988). Also see [954].

Page 645, Theorem 60.16: Both inequalities should be strict. The original references are the Mahmoodian-Soltankhah and Soltankhah references given above.

Page 645, Conjecture 60.18: The original references are the Mahmoodian-Soltankhah and Soltankhah references given above.

Page 651, Table 61.33: The entry in row 1, column 8, of the table should read "14" instead of "13".

Page 692, Theorem 1.128: 2-rank 31 should be 2-rank 27.

Page 811, Table 8.35: n is from 1 to 4, not to 5.

page 855-868, Table 11.12 Everywhere OA(k,n) appears in this table the values of k and n are transposed. So for example, on page 857, line 4, it was written OA(7,3) when it should have been OA(3,7).

Page 857, line -5: No S(2,6,46) exists.

Page 894, Reference 306. The year of publication should be 1939, not 1938.

Page 920, Reference 976. The complete reference should read: Some results on designs with repeated blocks, Vol 20 (1982), 15-37. (The complete name of the journal is Rostocker Mathematisches Kolloquium).

Page 938, Reference 1471 The authors of this paper should be should be C. J. Colbourn and A. C. H. Ling, not A. C. H. Ling and C. J. Colbourn. (Sorry Charlie).