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 IV of the Handbook.

Last edited 8/16/10

Page 256, Theorem 4.5. This theorem is now a special case of the
following theorem: Let *u*, *v* and *x* be positive
integers with *v* ≤ *u*. Then a 3-GDD of type
u^{1} v^{1} 1^{x} exists if and only if
*u*, *v* and *x* are odd, uv+ux+vx+\binom{x}{2} ≡
0 (mod 3), and *x* ≥ *u*. This result appears in Darryn
Bryant and Daniel Horsley, Steiner triple systems with two disjoint
subsystems, *J. Combin. Des.*, **14**, 14-24 (2006). Darryn
Bryant (db@maths.uq.edu.au) Sept. 2007.

Page 260, Theorem 4.32. The four possible exceptions with m = 3 and λ = 1, namely
(n,t) \in {(6,14), (6,15), (6,18), (6,23)}, were constructed directly by
Cao, Wang and Wei. The result appears in H. Cao, L. Wang, R. Wei, The existence of HGDDs with block size
four and its application to double frames, *Discrete Mathematics*, Volume 309,
Issue 4 (2009), Pages 945-949. Fei Gao (feigao.chn@gmail.com), March 2010.

Page 265, Theorem 5.44.
The 4-RGDD of type 12^{27} was found in Theorem 2.1 of
X. Sun and G. Ge, "Resolvable group divisible designs with block size
four and general index," Discrete Math. vol. 309, pp. 2982-2989, 2009.
http://dx.doi.org/10.1016/j.disc.2008.07.029. Fei Gao (feigao.chn@gmail.com), August 2010.

Page 265, Theorem 5.44. 4-RGDD of types 2^{142} , 2^{346}, 6^{54} and 24^{23} were found in
E. Schuster and G. Ge, "On uniformly resolvable designs with block sizes
3 and 4", Des. Codes Cryptogr., vol. 57, pp 45 -- 69, 2010.
http://dx.doi.org/10.1007/s10623-009-9348-1. Fei Gao (feigao.chn@gmail.com), August 2010.

Page 265, Theorem 5.45.
The {4,3}-RGDD of type 2^{54} was found in Theorem 2.2 of
X. Sun and G. Ge, "Resolvable group divisible designs with block size
four and general index," Discrete Math. vol. 309, pp. 2982-2989, 2009.
http://dx.doi.org/10.1016/j.disc.2008.07.029. Fei Gao (feigao.chn@gmail.com), August 2010.

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