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 III of the Handbook.

Last edited 1/19/17

Page 149, Remark 1.102. There is no Sudoku
critical set of size 16. The reference is: Gary McGuire, Bastian Tugemann, Gilles Civario, There
is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem, arXiv:1201.0749v1 (January 2012). Gordon Royle
has collected 49,151 distinct Sudoku critical sets of size 17. These can be accessed on his website http://mapleta.maths.uwa.edu.au/~gordon/sudokumin.php

Page 175, Table 3.83 and Page 176 Table 3.87.
In Table 3.83, i_{7} can be reduced to 618.
Here's how: For the 3 largest unknown cases, write

702 = 23.29 + 18 (spike) + 17

660 = 23.27 + 14 (spike) + 25

654 = 23.27 + 14 (spike) + 19

So there are 7 HMOLS of types 23^{28} 41^{1} 17^{1}
, 23^{26} 37^{1} 25^{1} and 23^{26} 37^{1}
19^{1} . Filling the holes with 0 extra points
respectively for v= 702, 660, 654 one obtains 7 idempotent MOLS for these
values. You can also get 660 from 7 HMOLS(8^{78}
35^{1} ) (660 = 8.79 + 27 + 1). Julian Abel

Page 176 Table 3.87. N(7968)
>= 31 (not 30). In 1969 Denniston showed there
exists a resolvable (v,32,1) BIBD for v = 7968 = 2^{13}
- 2^{8} + 2^{5}. This RBIBD gives the required MOLS. Julian Abel

Page 190, Table 3.102. This table should have
included 4 maxMOLS(9), since they appeared in reference [750]. Also, there
exists 2 maxMOLS(n) for all n>6 that aren't twice a prime > 7. So
"2" should be added as a value of k in Table 3.102 for all n > 6
except 22, 26, 34, 38, 58. The reference is P.Danziger, I.M.Wanless and B.S.Webb, "Monogamous Latin Squares", *J. Combin. Theory Ser. A ***118** (2011), 796--807. Ian Wanless (ian.wanless@monash.edu) Jan 2011.

Page 214, Theorem 5.23. An ISOLS(26,8)
has been found. See Example 2.8 in Hantao
Zhang, 25 new r-self-orthogonal Latin squares, *Discrete Math*. 313 (2013), 1746–1753.

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