This page contains new results in the area of
combinatorial designs that have occurred since the publication of the
*CRC Handbook of Combinatorial Designs *. The results here would
be contained in Part 1 of the Handbook (pages 1-94).

Last edited 5/22/05

Page 15, Design #29. Nd = 11,084,874,829 (instead of Nd $\ge $ 1.1x10^9). Reference: P. Kaski and P.R.J. Östergård, "The Steiner triple systems of order 19", submitted for publication. A preprint of the paper can be found at http://www.tcs.hut.fi/~pkaski/sts19.ps. Patric Östergård (patric.ostergard@hut.fi), December 2001.

Page 15, Design #32. Nd

Page 15, Design #34. Nd = 0 (instead of ?). Reference:
S.K. Houghten, L.H. Thiel, J. Janssen, and C.W.H. Lam, "There is no
(46,6,1) block design", * J. of Combinatorial Designs* **
9** (2001), pp 60 - 71.

Page 15, Design #42. Nd

Page 15, Design #45. Nd

Page 15, Design #46. Nd >= 22998 (Instead of Nd *Diskretnii Analiz i Issledovanie Operatsii*, vol.5,
N1 (1998), 64-81 (in Russian). Svetlana Topalova
(svetlana@moi.math.bas.bg), August 1998.

Page 15, Design #55. Nd = 242,995,846, and Nr = 74,700. Reference:
P. R. J. Östergård, "Enumeration of 2-(12,3,2) designs",
*Australas. J. Combin.* **22** (2000),
227-231. (Patric.Ostergard@hut.fi), May 2001.

Page 15, Design #56, Nr=5 (instead of Nr

Page 15, Design #66. Nr = 426. P. R. J. Östergård and P. Kaski, Enumeration of 2-(9,3,lambda) designs and their resolutions, submitted for publication. Patric Östergård (Patric.Ostergard@hut.fi), April 2000.

Page 15, Design #71. Nd = 13,769,944. Click here for more information about these designs. P. Denny (pden001@cs.auckland.ac.nz), Dec. 1997.

Page 15, Design #72. Nd *J. Combinatorics, Information and System Sciences*, No.3-4, 161-176 (1997).
Svetlana Topalova (svetlana@moi.math.bas.bg), August 1998.

Page 15, Design #75. Nd *Ars Combinatoria* 48 (1998), 135-146.
Svetlana Topalova (svetlana@moi.math.bas.bg), August 1998.

Page 16, Design #87. Nr

Page 16, Design #97. Nd *J.
Combinatorial Theory, Series A* (to appear). C. Lam (lam@cs.concordia.ca),
Jan. 2000.

Page 16, Design #99. Nr

Page 16, Design #102. Nd *Journal of Statistical Planning and
Inference*, 62(1997), 115-124. Ben Li (lipakc@cs.umanitoba.ca),
March 2003.

Page 16, Design #102. Nr = 0. (instead of ?). Reference: P. Kaski
and P. R. J. Östergård, "There exists no (15,5,4) RBIBD",
*J. Combin. Des.* **9** (2001), 227-232.
(Patric.Ostergard@hut.fi), May 2001.

Page 16, Design #108. Nd *Journal of Statistical Planning and
Inference*, 62 (1997), 115-124. Ben Li (lipakc@cs.umanitoba.ca),
March 2003.

Page 16, Design #123. Nd

Page 16, Design #124 Nd

Page 16, Design #128. Nd

Page 17, Design #140. Nd

Page 17, Design #143. Nd *J.
Combinatorial Theory, Series A* (to appear). C. Lam (lam@cs.concordia.ca),
Jan. 2000.

Page 17, Design #144. Nr

Page 17, Design #145. Nr = 149,041. P. R. J. Östergård and P. Kaski, Enumeration of 2-(9,3,lambda) designs and their resolutions, submitted for publication. Patric Östergård (Patric.Ostergard@hut.fi), May 2001.

Page 17, Design #146. Nd

a) 224 are cyclic (Ref [28]);

b) 12 are regular over V_{49} (Ref [48]);

c) 529 are obtainable by composition of a (33,3,1)-RBIBD with the affine
plane of order 16 (Ref: M. Buratti and F. Zuanni, "Composing a
(r(k-1)+1,k,1)-RBIBD with a (r,k+1,1)-BIBD", preprint).

d) 4 are 1-rotational over the group G =
(Z_{3})+(Z_{4})+(Z_{4})
(Ref: M. Buratti and F. Zuanni, "On singular 1-rotational difference
families"). The following blocks are representatives of the block-orbits
under G of one of these 1-rotational BIBD's:
{000, 100, 200, *}, {000, 010, 020, 030}, {000, 001, 002, 003},
{000, 011, 022, 033}, {000, 012, 102, 231}, {000, 013, 120, 221},
{000, 021, 103, 213}.

M. Buratti (buratti@mat.uniroma1.it), Dec. 1997. (Further report by
F. Zuanni (zuanni@ing.univaq.it), Feb. 1998.)

Page 17, Design #148. Nd

Page 17, Design #150. Nd = 270,474,142.
P. R. J. Östergård, There are 270,474,142 nonisomorphic
2-(9,4,6) designs, *Journal of Combinatorial Mathematics and
Combinatorial Computing*, 37 (2001), pp 173-176. Patric
Östergård (Patric.Ostergard@hut.fi), April 2000.

Page 17, Design #158. Nd

Page 17, Design #170. Nd

Page 17, Design #173. Nr

Page 17, Design #174. Nr

Page 17, Design #174. Nr

Page 17, Design #176. Nd

Page 17, Design #185. Nd

Page 18, Design #199. Nd

Page 18, Design #205. Nd *Journal of Combinatorial
Designs* 8 (2000), 261-273, Luis B. Morales (lbm@servidor.unam.mx)
March 2000.

Page 18, Design #208. Nd

Page 18, Designs #219. Nr

Page 18, Design #220. Nd

Page 18, Design #221. Nd

Page 18, Design #233. Nd ^{14}
(instead of Nd *J. Combinatorial Theory, Series
A* (to appear). C. Lam (lam@cs.concordia.ca), Jan. 2000.

Page 18, Design #235. Nd = 5,862,121,434 and Nr = 203,047,732. P. R. J. Östergård and P. Kaski, Enumeration of 2-(9,3,\lambda) designs and their resolutions, submitted for publication. Patric Östergård (Patric.Ostergard@hut.fi), May 2001.

Page 18, Design #242. Nd *Europ. J. Combin.* 13(1992),
515-520. June 1997. Nd

Page 18, Design #246. Nd

Page 19, Design #255. Nd *J. Comb. Des.* 8 (2000), 261-273, Luis
B. Morales (lbm@servidor.unam.mx) March 2000.

Page 19, Design #256. Nd *J. Comb. Des.* 8 (2000), 261-2738 (2000),
261-2738 (2000), 261-273, Luis B. Morales (lbm@servidor.unam.mx) March
2000.

Page 19, Design #278. Nd = 8,360,901 (Not 5,201,971) Click here for more information about these designs. P. Denny (pden001@cs.auckland.ac.nz), Dec. 1997.

Page 19, Design #279. Nd

Page 19, Design #291. Nd

Page 19, Design #300. Nd *J.
Combinatorial Theory, Series A *(to appear). C. Lam
(lam@cs.concordia.ca), Jan. 2000.

Page 20, Design #312. Nd

Page 20, Design #326. Nd *J. Comb. Des.* 8 (2000), 261-273, Luis
B. Morales (lbm@servidor.unam.mx) March 2000.

Page 20, Design #351, Nd

Page 21, Design #376. Nd

Page 21, Design #407. Nd _{2}. Among them there are four
self-dual and nine pairs of dual designs. Full automorphism groups of
those designs are isomorphic to Frob21 x Z_{2}. One of
self-dual designs is isomorphic to the design constructed by Z. Janko
and Tran van Trung the other designs are new. Dean Crnkovic
(deanc@pefri.hr) Sept. 1999.

Page 21, Design #410. Nd

Page 21, Design #412. Nd

A new design is 1-rotational over the group G =
(Z_{2})+(Z_{2})+(Z_{5})+(Z_{5}).
(Ref: Same as for designs #146c above). The following blocks are
representatives for the block-orbits under G of this design:
{0000,1000,0100,1100,*},{0000,0011,0022,0033,0044},{0000,0012,0024,0031,0043},
{0000,0013,0021,0034,0042},{0000,0014,0023,0032,0041},
{0000,0010,1014,0104,1133}, {0000,0004,1024,0120,1142},
{0000,0020,1023,0103,1111}, {0000,0003,1043,0140,1134}. M. Buratti
(buratti@mat.uniroma1.it), Dec. 1997.

Page 22, Design #448. Nr

Page 22, Design #451. Nr = 1,363,486 (instead Nr *J. Combin. Math. Combin. Comput. *47 (2003), 65--74.

Page 22, Design #452. Nd

Page 23, Design #513. Nd

Page 23, Design #526. Nd

Page 25, Design #574. This design (with parameters 2-(175,7,1)) has been found by Janko and Tonchev. Contracting that design gives a generalized Bhaskar-Rao design GBRD(25,100, 28,7,1,Z7) (See page 241 in the Handbook). (tonchev@math.mtu.edu). July 1997.

Page 25, Design #624. Nd

Page 25, Design #630. Nd *J. Comb. Des.* 8 (2000), 261-273, Luis
B. Morales (lbm@servidor.unam.mx) March 2000.

Page 26, Design #661. Nd

Page 26, Design #662. Nd

Page 26, Design #682. Nr

Page 26, Design #684. $Nd\; \ge \; 5,985$ (instead of $Nd\; \ge \; 2$) M. Buratti (buratti@mat.uniroma1.it), March 2002.

Page 26. Design #685. $Nd\; \ge \; 770$ (instead of $Nd\; \ge \; 237$) (F. Zuanni (zuanni@ing.univaq.it), May 1998.

Page 27, Design #736. Nd

Page 28. Design #789. $Nr\; \ge \; 1$. R. Julian R. Abel (julian@maths.unsw.edu.au), Nov. 1998.

Page 29, Design #823. Nd

Page 29, Design #829. A design with parameters (106,7,2) has been shown to exist (This also updates Table 2.8). R. Julian R. Abel (julian@maths.unsw.edu.au), March 1998.

Page 29, Design #837. Nr *Journal of Combinatorial Mathematics and
Combinatorial Computing* 36 (2001), 119-126.
Luis B. Morales (lbm@servidor.unam.mx) March 2000.

Page 29, Design #840: Nd

Page 30, Design #873. Nd

Page 30, Design #880. Nd ^{14} and Nr ^{5}. P. R. J. Östergård and P. Kaski,
Enumeration of 2-(9,3,lambda) designs and their resolutions,
submitted for publication. Patric Östergård
(Patric.Ostergard@hut.fi), May 2001.

Page 30, Design #882. $Nd\; \ge \; 16,987,430,331,445$ (instead of $Nd\; \ge \; 2$). This may be obtained combining the update on design #32 given above by Vedran Krcadinac with a result by Buratti and Zuanni (Disc. Math. 238). M. Buratti (buratti@mat.uniroma1.it), March 2002.

Page 30, Design #889. Nr *Australasian
J. Comb.* 15(1997), 177-202)

Page 30, Design #891. Nr = 27,121,734 (instead of Nr *J. Combinatorial Designs*, to appear).

Page 30, Design #896. A cyclic difference family for this design has been added to the web page http://www.emba.uvm.edu/~dinitz/newresults.part4.html under Page 273 -- Example 10.10.

Page 31. Design #972. Nd

Page 32, Design #1030. Nd = 1033129 (instead of >417). (Mathon, Pietsch). Reference: #90 on page 39 of the Handbook.

Page 32, Design #1033. This design (with parameters (196,6,1)) exists. R. Julian R. Abel (julian@maths.unsw.edu.au), Dec. 1997.

Page 33, Design 1040. Nd

Page 33, Design #1042. Nr *Journal of Combinatorial Mathematics and
Combinatorial Computing* 36 (2001), 119-126.
Luis B. Morales (lbm@servidor.unam.mx) March 2000.

Page 33, Design #1074. Nd

Page 33. Design #1079. Nd ^{13} (instead of Nd ^{7}). (Ref:
Same as for designs #146c above). M. Buratti
(buratti@mat.uniroma1.it), Dec. 1997.

Page 34, Design #1096. This design (with parameters (201,6,1)) exists. R. Julian R. Abel (julian@maths.unsw.edu.au), Dec. 1997.

Page 34, Design #1102. Nd

Page 35, Design #1171. This symmetric design (with parameters (105,40,15)) has just been found by Zvonimir Janko. A description of it can be found here . (janko@mathi.uni-heidelberg.DE)

Page 35, Design #1174. Nd

Page 37, Reference [44]. This paper published in JCMCC 27(1998), 33-52. Malcolm Greig (greig@sfu.ca) Jan 1999.

Page 42, Table 2.3. When k=7 and lambda = 1, replace 4387 by 2605. R. Julian R. Abel (julian@maths.unsw.edu.au)

Page 42, Theorem 2.4 and Table 2.8: A (253,7,lambda) BIBD exists
for lambda = 2 (and hence for all lambda

Page 42, Table 2.5. 141, 276, 706, 741, 766, can all be deleted; also 1221 and 1251 are the only possible exceptions > 801. (Abel, Greig, Mills) (julian@maths.unsw.edu.au), May 1997. (v,6,1) BIBDs exist for v=196, 201, 1221, 1251, leaving v=801 the largest unknown case. R. Julian R. Abel (julian@maths.unsw.edu.au), Dec. 1997.

Page 42, Table 2.6. 61, 66, 67, 83 can be deleted. R. Julian R. Abel (julian@maths.unsw.edu.au)

Page 42, Table 2.6. 29 can be deleted. This design exists as a consequence of the existence of design no. 574 on page 25. Vladimir Tonchev. (tonchev@math.mtu.edu). July 1997.

Page 42, Table 2.7. 4 can be deleted. (See item above concerning page 25, design no. 574.). Also the value 29 can be deleted as a consequence of the existence of the design with t=4. Vladimir Tonchev. (tonchev@math.mtu.edu). July 1997.

Page 42, Table 2.7. 6 can be deleted (i.e: a (259,7,1) BIBD exists). R. Julian R. Abel (julian@maths.unsw.edu.au) Sept. 1997.

Page 42, Table 2.7. 44 can be deleted (Greig). (julian@maths.unsw.edu.au), May 1997.

Page 43, Table 2.11. The values t=8, 72, 93, 97, 107, 128, 197, 212, 219 can be removed from this table (Greig). The t=8 design is a (577,9,1) difference family found by M. Buratti; this difference family removes 1 exception in Theorem IV.10.53, page 281. (julian@maths.unsw.edu.au), May 1997.

Page 43, Table 2.12. The values t= 20 and t=60 can be removed from
this table (M. Buratti and F. Zuanni, *G-invariantly resolvable
Steiner 2-designs which are 1-rotational over G*, preprint.) Both
of these designs are 1-rotational. Click
here for the base blocks of both of these designs.
(buratti@mat.uniroma1.it), Sept. 1997

Page 43, Remark 2.17. t=39, 50, 51 can be deleted when k=6. R. Julian R. Abel (julian@maths.unsw.edu.au)

Page 43, Table 2.14. A (358,8,4) BIBD exists. (greig@sfu.ca) Aug. 1999. (v,8,4) BIBDs exist for v=85, 99, 155, 358, 365 and (v,8,2) BIBDs exist for v=141, 148. (Abel, Bluskov, Greig), November 1999.

Page 43, Table 2.14. A (358,8,4) BIBD exists. (greig@sfu.ca) Aug. 1999. (v,8,4 ) BIBDs exist for v=85, 99, 155, 358, 365 and (v,8,2) BIBDs exist for v=141, 148. (Abel, Bluskov, Greig), November 1999. Abel, Bluskov & Greig have now shown that (274,8,4) and (323,8,4) BIBDs exists, so (v,8,4) BIBDs exist for all v = 1 mod 7 with the possible exception of v=22. (greig@sfu.ca) Jan. 2000.

Page 43. As a consequence of the revision of (v,8,7) NRBs (see the new results for I.6.23), and a grouplet construction of a (385,9,9) BIBD, One gets: If the necessary condition v \equiv 1 (mod 8) holds, then a (v,9,9) BIBD exists, except possibly for v=553. Abel, Finizio, Greig, Lewis. (greig@sfu.ca) Aug. 1999.

Page 43, Table 2.15: A (135,9,4) BIBD exists and (v,9,8) BIBDs exist for v=54, 198, 315, 1278. (Abel, Bluskov, Greig), November 1999.

Page 43, Remark 2.20. Now that 5 MOLS(42) are known (See Theorem
II.2.54), there exists a 7-GDD of type 42^{t} for t= 7, in
addition to the known t=8,9. Hence if t is in B({7,8,9}), there is
a a 7-GDD(42^{t}). From the table on P209, this means
there is a 7-GDD(42^{t}) for t=58 and for 63 <= t <= 92. R. Julian
R. Abel (julian@maths.unsw.edu.au)

Page 50, Table 3.31. There exists an infinite family of 3-(q+1, (q+1)/2, (q+1)(q-3)/8)designs, where q is a prime power congruent to 3(mod 4). Reference: S. Iwasaki, An elementary and unified approach to the Mathieu-Witt systems, J. Math.Soc.Japan 40(1988),393-414. S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 54, Table 3.37. There does not exist a 3-(22,10,6) design (and also there is no 3-(37,16,8) design). This was proved in the Ph.D. thesis of J"orn Bolick at Hamburg University. Reported by H.-D. Gronau (gronau@zeus.math.uni-rostock.de). Dec. 19, 1997.

Page 56, Table 3.37. There exists a 3-(24, 12, 12.5) design. This results when q=23 in the theorem by S. Iwasaki mentioned above (Page 50, Table 3.31). S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 56, Table 3.37. There exists a 3-(26, 9, 3.21) design. Reference: S. Iwasaki and T. Meixner A remark on the action of PGL(2, q) and PSL(2, q) on the projective line, Hokkaido Math.J. 26 (1997), 203-209. S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 57, Table 3.37. There exists a 3-(26, 13, 13.11) design, a 3-(28, 14, 28.6) and a 3-(30, 5, 5.3) design. Reference: S. Iwasaki and T. Meixner A remark on the action of PGL(2, q) and PSL(2, q) on the projective line, Hokkaido Math.J. 26 (1997), 203-209. S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 57, Table 3.37. There exists a 3-(28, 14, 14.6) design. This results when q=27 in the theorem by S. Iwasaki mentioned above (Page 50, Table 3.31). S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 57, Table 3.37. There exists a 3-(30, 8, 4.6) design and a 3-(30,8, 8.6) design. Reference: S. Iwasaki, Infinite families of 2- and 3-designs with parameters ... , JCD 5(1997), 95-110. S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 58, Table 3.37. There exists a 3-(30, 15, 15.13) design. Reference: S. Iwasaki, Infinite families of 2- and 3-designs with parameters ... , JCD 5(1997), 95-110. S. Iwasaki (iwasaki@math.hit-u.ac.jp). April 2002.

Page 59-60, Table 3.37. There exist simple 5-(24,10,lambda) designs for lambda=18m, 6<= m <=52 and m = 4. These designs all admit PSL(2,23). These designs are 4-(24,10,60m) designs with 6<= m <=52 and m = 4. In addition, there exist 4-(24,10,60m) designs for m=3, 5, 53, 54, 55. Masaaki Kitazume and Akihiro Munemasa (munemasa@math.kyushu-u.ac.jp). May 28, 1997.

Page 60, Table 3.37. A simple 5-(24,10,36) design has been found by T.A. Gulliver and Masaaki Harada. (harada@math.okayama-u.ac.jp)

Page 62, Remark 3.38. New simple 7-designs and 8-designs have been found by Betten, Laue and Wassermann. Click here for their web page. It contains a wealth of valuable information concerning these designs and the software package DISCRETA which was used to find them. In particular, Alfred Wassermann has just found some very interesting new ones: 7-(20,10,lambda), lambda = 116,124,134. Also found are 8-(31,10,93) and 8-(31,10,100), both with automorphism group PSL(3,5).

Page 63, Table 3.44. There exists a large set LS_360(3,10,24) with automorphism group PSL(2,23). Note there are 323 3-(24,10,360) designs comprising this large set. Anton Betten (anton@btm2xf.mat.uni-bayreuth.de).

Page 79, Known Symmetric Designs. Let q and r = (q^d - 1)/(q - 1) be prime powers. For any positive integer m, there exists a symmetric (v,k,lambda)-design with v = qr (r^{m+1} - 1)/(r - 1) + 1, k = r^{m+1}, lambda = r^m (r - 1)/q. If d = 2, these are precisely the parameters of Family 10. Designs with q = 2 are contained in Family 11. The case q = 8, d = 3 was reported by Yury Ionin earlier. Otherwise, the parameters are new. Yury Ionin (yury.ionin@cmich.edu). Nov. 1998.

Page 79, Known Symmetric Designs. In Family 12, "p a prime" can be replaced by "p a prime power". Yury Ionin (yury.ionin@cmich.edu). Feb. 1997.

Page 79, Known Symmetric Designs. A new infinite class of symmetric designs has the following parameters: v = (73^(m+1) - 64)/9, k = 73^m, lambda = 9x73^(m-1), n = 64x73^(m-1) (m is a positive integer). Yury Ionin (yury.ionin@cmich.edu).

Page 79, Known Symmetric Designs. A new infinite class of symmetric designs has the following parameters: v = (2(q+1)^(2m+1) - q)/(q+2), k = q((q+1)^(2m) - 1)/(q+2), lambda = (q^2(q+1)^(2m-1) - 2q)/(2q+4), n = q(q+1)^(2m-1)/2, where q = 2^p - 1 is a Mersenne prime, m is a positive integer. (For the complementary design, k = (q+1)^(2m), lambda = (q+2)(q+1)^(2m-1)/2). If q = 3, then it is the family claimed by J.D.Fanning in the note "A family of symmetric designs", Discrete Math. 146 (1995), 307-312. Also note that in the case m=1, this family corresponds to a subcase for m=2 of the Family 11 (Wilson and Brouwer) in the Handbook. Yury Ionin (yury.ionin@cmich.edu).

Page 79, Known Symmetric Designs. If m and d are positive integers, p is an arbitrary prime power, and q is a prime power that is specified below, then there exist symmetric designs with the following parameters:

b) v = 2.3^d(q^(2m)-1)/(3^d+1), k = 3^dq^(2m-1), lambda = 3^d(3^d+1)q^(2m-2)/2, q = (3^(d+1)+1)/2;

c) v = 3^d(q^(2m)-1)/(2(3^d-1)), k = 3^d(3^dq^(2m-1)-1)/(2(3^d-1)), lambda = 3^d(3^(2d)q^(2m-2)-1)/(2(3^d-1)), q = 3^(d+1)-2.

All these designs are new if m > 1. If m = 1, then design a) is in Family 12, designs b) and c) are in Family 9. Yury Ionin (yury.ionin@cmich.edu). Feb. 1997.

Page 79, Known Symmetric Designs. v = 2^(2d+3)(q^(2m)-1)/(q+1), k = 2^(2d+1)q^(2m-1), lambda = 2^(2d-1)(q+1)q^(2m-2), where d and m are positive integers and q = (2^(2d+3)+1)/3 is a prime power. For m = 1, these designs belong to the Davis-Jedwab family of difference sets (q does not have to be a prime power there); for m > 1, they are new. Yury Ionin (yury.ionin@cmich.edu). Nov. 1997.

Page 79, Known Symmetric Designs. v = 2^(2d+3)(q^(2m)-1)/(3q-3), k = 2^(2d+1)q^(2m-1), lambda = 2^(2d-1)(3q-3)q^(2m-2), where d and m are positive integers and q = 2^(2d+3)-3 is a prime power. For m = 1, these design are the complements of the designs from the previous family; for m > 1, they are new. Yury Ionin (yury.ionin@cmich.edu). Nov. 1997.

Page 79, Known Symmetric Designs. v = h((2h-1)^{2m}-1)/(h-1), k = h(2h-1)^{2m-1}, lambda = h(h-1)(2h-1)^(2m-2), where m is a positive integer, h = 3.2^d or -3.2^d (d is a nonnegative integer), and |2h-1| is a prime power. For m = 1, these designs belong to the Menon family; for d = 0, they belong to the family that is listed above on this web page (p. 79(b,c)). If m > 1 and d > 0, they are new. Yury Ionin (yury.ionin@cmich.edu). Nov. 1997.

Page 79, Known Symmetric Designs. There is a new family of
symmetric designs that was obtained by the combined efforts of
Kharaghani (2 papers), Janko, Karaghani and Tonchev (two papers),
Ionin and Kharaghani, and Ionin. All references can be found in the
paper by Yury Ionin titled "Regular Hadamard matrices generating
infinite families of symmetric designs". This paper will appear in the
journal *Designs, Codes and Cryptography*.
Click here for the parameters of these
designs. Yury Ionin (yury.ionin@cmich.edu). Oct. 2003.

Page 79, Known Symmetric Designs (Family 9). There are two series of symmetric designs with parameters (3^m(3^m-1)/2, 3^m-1(3^m +1)/2, 3^m-1(3^m-1 +1)/2) and (3^m(3^m +1)/2, 3^m-1(3^m -1)/2, 3^m-1(3^m-1 -1)/2) respectively. Both series admit the orthogonal groups O(2m+1,3) as groups of automorphisms. In both cases O(2m+1,3) acts on points and lines transitive as a rank 3 permutation group. The representations on points and lines are in both cases equivalent. U. Dempwolff (dempwolff@mathematik.uni-kl.de) Jan. 1999.

Page 80, Section I.5.6. A new symmetric design with parameters (105,40,15) has been found by Zvonimir Janko. A description of it can be found here. (janko@mathi.uni-heidelberg.DE). November 25, 1996.

Page 80, Section I.5.6. There are at least 52432 symmetric (100,45,20) designs on which Frob_10 x Z_2 acts as an automorphism group. These designs correspond to 52432 Bush-type Hadamard matrices. Each Bush-type Hadamard matrix leads to an infinite class of twin designs with parameters v=100(81^m + ... + 81 + 1), k=45(81)^m, lambda=20(81)^m, and Siamese twin designs with parameters v=100(121^m + ... + 121 + 1), k=55(121)^m, lambda=30(121)^m, where m is an arbitrary positive integer. Dean Crnkovic and Dieter Held (deanc@pefri.hr, held@mathematik.uni-mainz.de). February 2001.

Page 80, Section I.5.6. There exists a symmetric design with parameters (144,66,30) whose full automorphism group is isomorphic to Aut M_12, the extension of the sporadic simple Mathieu group on 12 letters by an automorphism of order two. The design can be obtained as follows: Let G=M_12 . In G there are exactly 144 subgroups isomorphic to PSL(2,11); denote them by L_1 , ... , L_144 . Define an incidence structure D=(P,B,I) as follows: P = { P_1 , ... , P_144 } , B = { B_1 , ... , B_144 } , P_i I B_j <=> | L_i \cap L_j | = 10 ; 1 <= i,j <= 144 . Then D is a symmetric (144,66,30) design. The full automorphism group of D is Aut M_12 and has order 190,080. Wolfram Wirth (wirth@mathematik.uni-kl.de).Oct. 1999.

Page 80, Section I.5.6. Two additional symmetric design with parameters (144,66,30) have been found. Click here for the construction. Wolfgang Lempken (lempken@werner.exp-math.uni-essen.de) December 1999.

Page 80, Section I.5.6. A new symmetric design with parameters (189,48,12) has just been found by Zvonimir Janko. A description of it can be found here. (janko@mathi.uni-heidelberg.DE). March 1997.

Page 80, Section I.5.6. There are exactly 54 symmetric (196,91,42) designs admitting an automorphism group isomorphic to Frob_{13*6} x Z_3 acting with orbit size distribution (1,13,13,13,39,39,39,39) for blocks and points. For 50 of these designs the full automorphism group has order 234 and is isomorphic to Frob_{13*6} x Z_3. The remaining four design have Frob_{13*6} x Frob_{7*3} as full automorphism group. Among these designs there are 18 self-dual designs and 18 pairs of mutually dual ones. The derived designs (with respect to the fixed block) of the four designs with full automorphism group of order 1638 are cyclic. Dean Crnkovic (deanc@mapef.pefri.hr). May 2005.

Page 80, Section I.5.6. There are exactly 10 symmetric
(324,153,72)-designs admitting an automorphism group isomorphic to
Frob_{19*9} x Z_{2} acting with orbit distribution
1,19,38,38,38,38,38,38,38,38. For eight of these designs the full
automorphism group has order 342 and is isomorphic to Frob_{19*9} x Z_{2},
one design has Frob_{19*9} x Z_{4} and the remaining design
Frob_{19*9} x Z_{8} as full automorphism group. All 10 designs are
self-dual. The derived design (with respect to the fixed block) of the
design with the full automorphism group of order 1368 is 1-rotational.
Dean Crnkovic and Dieter Held
(deanc@mapef.pefri.hr, held@mathematik.uni-mainz.de). April 2004.

Page 80, Section I.5.6. There is a symmetric (14080,1444,148) design which admits the sporadic simple Fischer group Fi(22) as a group of automorphisms. Fi(22) acts transitive as a rank 3 permutation group on points and lines. The two permutation representations are inequivalent. U. Dempwolff (dempwolff@mathematik.uni-kl.de) Jan. 1999.

Page 90, Theorem 6.17. For k even, if v = k mod (k(k-1)) and v > exp(exp(k^18k^2), then a (v,k,1) RBIBD exists. (The existence of resolvable BIBD with k even and lambda = 1, Chang Yanxun, preprint).

Page 90, Table 6.19. When k=5 and lambda = 1, replace 4905 by 645. R. Julian R. Abel (julian@maths.unsw.edu.au). May 1997.

Page 90, Table 6.19. (v,5,2) RBIBDs exist for all v=5 mod 10 except for v=15 and possibly for v in {45,115,135, 195,215,225, 235,295,315, 335,345,395}. R. Julian R. Abel (julian@maths.unsw.edu.au). March 1998.

Page 90, Table 6.19. When k=5 and lambda=4, the value 15 should be
added to the Exceptions. Reference: P. Kaski and
P. R. J. Östergård, "There exists no (15,5,4) RBIBD",
*J. Combin. Des.* **9** (2001), 227-232. Patric
Östergård (Patric.Ostergard@hut.fi), May 2001.

Page 91, Table 6.21. 45, 225, 345, 465, 645 are the only possible exceptions for (v,5,1) RBIBDs (Abel, Greig) R. Julian R. Abel (julian@maths.unsw.edu.au). May 1997. and M. Greig (greig@sfu.ca) Nov. 1997.

Page 91, Tables 6.21 and Table 6.22. (75,5,2) and (185,5,1) RBIBDs exist. M. Greig (greig@sfu.ca) Nov. 1997.

Page 91, Table 6.22. A (15,5,4) RBIBD does not exist. Reference:
P. Kaski and P. R. J. Östergård, "There exists no (15,5,4)
RBIBD", *J. Combin. Des.* **9** (2001), 227-232. Patric
Östergård (Patric.Ostergard@hut.fi), May 2001.

Page 91, Table 6.23: (v,6,5) RBs have been found for v= 48, 60, 138, 318, 330, 336, 414 and 594. R. Julian R. Abel (julian@maths.unsw.edu.au). April 1999 and April 2000.

Page 91, Table 6.25. A (616,8,7) RBIBD exists. M. Greig, Nov. 1997. A (504,8,7) RBIBDs exist. M. Greig (greig@sfu.ca) Aug. 1999.

Page 91, Table 6.26. A (145,6,5) NRB exists. So do (v,7,6) NRBs for v= 85, 99, 141, 148, 589, 596, 603. R. Julian R. Abel (julian@maths.unsw.edu.au). Sept. 1998.

Page 91: Table 6.26: (v,6,5) NRBs exists for all v = 1 mod 6. (v,7,6) NRBs exists for all v=1 mod 7 except possibly for v=183,246,267,274,295. (v,8,7) NRBs exists for all v=1 mod 8 except possibly for v=161,321,385,481,553. R. Julian R. Abel (julian@maths.unsw.edu.au). April, 1999.

Page 91, Table 6.26. A (545,8,7) NRB exists as does a cyclic (129,8,7) NRB. R. Julian R. Abel (julian@maths.unsw.edu.au). March 1998 and Oct. 1998.

Page 91, Table 6.26: (v,8,7) NRBs exist for 161, 321, 481, leaving 385, 553 the only open cases. R. Julian R. Abel (julian@maths.unsw.edu.au). August 1999.

Page 93, Reference [1] has appeared in *Des. Codes Cryptogr.* 11
(1997) 123--140. (greig@sfu.ca) Aug. 1999.

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