Some new uniform frames with block size four and index one or three

Journal of Combinatorial Designs

Volumn 12, Issue 2, 2004, Pages 112-122

  Ge, Gennian ^a   Lam, C W H ^b   Ling, Alan C H ^c  

^a ZHEJIANG UNIVERSITY   (China)

^b Dept of Electrical and Computer Engineering   (Canada)

^c University of Vermont ^*  (United States)

Author keywords

Frames; Group divisible designs; Resolvability

Indexed keywords

EID: 1542304725     PISSN: 10638539     EISSN: 15206610     Source Type: Journal    
DOI: 10.1002/jcd.10054     Document Type: Article

References (16)

1. R. J. R. Abel and A. M. Assaf, Modified group divisible designs with block size 5 and γ = 1, Discrete Math 256 (2002), 1-22.
2. F. E. Bennett, C. J. Colbourn, and R. C. Mullin, Quintessential pairwise balanced designs, J Stat Plann Infer 72 (1998), 15-66.
3. T. Beth, D. Jungnickel, and H. Lenz, Design Theory, Cambridge University Press, 1986.
4. C. J. Colbourn and J. H. Dinitz, CRC Handbook of Combinatorial Designs, CRC Press Inc., Boca Raton, 1996. New results are reported at http://www.emba.uvm.edu/dinitz/newresults.html
5. Y. Chang and Y. Miao, General constructions for double group divisible designs and double frames, Des Codes Cryptogr 26 (2002), 155-168.
6. C. J. Colbourn, D. R. Stinson, and L. Zhu, More frames with block size four, J Combin Math Combin Comput 23 (1997), 3-20.
7. S. C. Furino, S. Kageyama, A. C. H. Ling, Y. Miao, and J. X. Yin, Frames with block size four and index three, J Stat Plann Infer 106 (2002), 117-124.
8. S. C. Furino, Y. Miao, and J. X. Yin, Frames and Resolvable Designs: Uses, Constructions and Existence, CRC Press, Boca Raton, FL, 1996.
9. G. Ge, Uniform frames with block size four and index one or three, J Combin Designs 9 (2001), 28-39.
10. G. Ge, R. S. Rees, and L. Zhu, Group-divisible designs with block size four and grouptype gum1 with m as large or as small as possible, J Comb Theory Ser A 98 (2002), 357-376.
11. H. Hanani, Truncated finite planes, Proc Symp Pure Math (A. M. S.) 19 (1971), 115-120.
12. E. R. Lamken,W. H. Mills, and R. Rees, Resolvable minimum coverings with quadruples, J Combinatorial Designs 6 (1998), 431-450.
13. R. S. Rees, Group divisible designs with block size k having k ) 1 groups, for k = 4 and 5, J Combin Designs 8 (2000), 363-386.
14. R. Rees and D. R. Stinson, Frames with block size four, Canad J Math 44 (1992), 1030-1049.
15. R. M. Wilson, Concerning the number of mutually orthogonal Latin squares, Discrete Math 9 (1974), 181-198.
16. J. Yin, A. C. H. Ling, C. J. Colbourn, and R. J. R. Abel, The existence of uniform 5-GDDs, J Combin Designs 5 (1997), 275-299.