Frontiers of Mathematics in China >
Super-simple (5, 4)-GDDs of group type gu
Received date: 16 Oct 2012
Accepted date: 29 May 2014
Published date: 26 Aug 2014
Copyright
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple group divisible designs are useful in constructing other types of super-simple designs which can be applied to codes and designs. In this article, the existence of a super-simple (5, 4)-GDD of group type gu is investigated and it is shown that such a design exists if and only if u≥5, g(u - 2)≥12, and u(u - 1)g2 ≡ 0 (mod 5) with some possible exceptions.
Guangzhou CHEN , Kejun CHEN , Yong ZHANG . Super-simple (5, 4)-GDDs of group type gu[J]. Frontiers of Mathematics in China, 2014 , 9(5) : 1001 -1018 . DOI: 10.1007/s11464-014-0393-3
| 1 |
Abel R J R, Bennett F E. Super-simple Steiner pentagon systems. Discrete Math, 2008, 156(5): 780-793
|
| 2 |
Abel R J R, Bennett F E, Ge G. Super-simple holey Steiner pentagon systems and related designs. J Combi<?Pub Caret?>n Des, 2008, 16(4): 301-328
|
| 3 |
Adams P, Bryant D, Khodkar A. On the existence of super-simple designs with block size 4. Aequationes Math, 1996, 52: 230-246
|
| 4 |
Alderson T L, Mellinger K E. 2-dimensional optical orthogonal codes from singer groups. Discrete Appl Math, 2009, 157(14): 3008-3019
|
| 5 |
Bluskov I. New designs. J Combin Math Combin Comput, 1997, 23: 212-220
|
| 6 |
Bluskov I, Hämäläinen H. New upper bounds on the minimum size of covering designs. J Combin Des, 1998, 6(1): 21-41
|
| 7 |
Bush K A. Orthogonal arrays of index unity. Ann Math Stat, 1952, 23: 426-434
|
| 8 |
Cao H, Chen K, Wei R. Super-simple balanced incomplete block designs with block size 4 and index 5. Discrete Math, 2009, 309(9): 2808-2814
|
| 9 |
Cao H, Yan F. Super-simple group divisible designs with block size 4 and index 5. Discrete Math, 2009, 309(16): 5111-5119
|
| 10 |
Cao H, Yan F. Super-simple group divisible designs with block size 4 and index 3, 4, 6. J Statist Plann Inference, 2010, 140(5): 1330-1345
|
| 11 |
Cao H, Yan F, Wei R. Super-simple group divisible designs with block size 4 and index 2. J Statist Plann Inference, 2010, 140(9): 2497-2503
|
| 12 |
Chen K. On the existence of super-simple (v, 4, 3)-BIBDs. J Combin Math Combin Comput, 1995, 17: 149-159
|
| 13 |
Chen K. On the existence of super-simple (v, 4, 4)-BIBDs. J Statist Plann Inference, 1996, 51(3): 339-350
|
| 14 |
Chen K, Cao Z, Wei R. Super-simple balanced incomplete block designs with block size 4 and index 6. J Statist Plann Inference, 2005, 133(2): 537-554
|
| 15 |
Chen K, Chen G, Li W, Wei R. Super-simple balanced incomplete block designs with block size 5 and index 3. Discrete Appl Math, 2013, 161: 2396-2404
|
| 16 |
Chen K, Sun Y G, Zhang Y. Super-simple balanced incomplete block designs with block size 4 and index 8. Util Math, 2013, 91: 213-229
|
| 17 |
Chen K, Wei R. Super-simple (v, 5, 5) designs. Des Codes Cryptogr, 2006, 39: 173-187
|
| 18 |
Chen K, Wei R. Super-simple (v, 5, 4) designs. Discrete Appl Math, 2007, 155(8): 904-913
|
| 19 |
Chen K, Wei R. On super-simple cyclic 2-designs. Ars Combin, 2012, 103: 257-277
|
| 20 |
Chung F R K, Salehi J A, Wei V K. Optical orthogonal codes: design, analysis and applications. IEEE Trans Inform Theory, 1989, 35: 595-604
|
| 21 |
Colbourn C J, Dinitz J H, eds. Handbook of Combinatorial Designs. 2nd ed. Boca Raton: Chapman & Hall/CRC, 2007
|
| 22 |
Gronau H-D O F, Kreher D L, Ling A C H. Super-simple (v, 5, 2) designs. Discrete Appl Math, 2004, 138: 65-77
|
| 23 |
Gronau H-D O F, Mullin R C. On super-simple 2-(v, 4, λ) designs. J Combin Math Combin Comput, 1992, 11: 113-121
|
| 24 |
Hartmann S. On simple and super-simple transversal designs. J Combin Des, 2000, 8(5): 311-320
|
| 25 |
Hartmann S. Superpure digraph designs. J Combin Des, 2000, 10(4): 239-255
|
| 26 |
Ji L, Yin J. Constructions of new orthogonal arrays and covering arrays of strength three. J Combin Theory Ser A, 2010, 117: 236-247
|
| 27 |
Julian R, Abel R J R. Existence of five MOLS of orders 18 and 60. J Combin Des,
|
| 28 |
Khodkar A. Various super-simple designs with block size four. Australas J Combin1994, 9: 201-210
|
| 29 |
Kim H K, Lebedev V. On optimal superimposed codes. J Combin Des, 2004, 12(2): 79-91
|
| 30 |
Ling A C H, Zhu X J, Colbourn C J, Mullin R C. Pairwise balanced designs with consecutive block sizes. Des Codes Cryptogr, 1997, 10: 203-222
|
| 31 |
Stinson D R, Wei R, Zhu L. New constructions for perfect hash families and related structures using related combinatorial designs and codes. J Combin Des, 2000, 8(3): 189-200
|
| 32 |
Todorov D T. Four mutually orthogonal Latin squares of order 14. J Combin Designs, 2012, 20(8): 363-367
|
| 33 |
Zhang Y, Chen K. Super-simple group divisible designs with block size 4 and index 9. J Statist Plann Inference, 2011, 141(9): 3231-3243
|
| 34 |
Zhang Y, Chen K, Sun Y. Super-simple balanced incomplete block designs with block size 4 and index 9. J Statist Plann Inference, 2009, 139(10): 3612-3624
|
/
| 〈 |
|
〉 |