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Volumn 60, Issue , 2001, Pages 3-54

Recursive constructions of balanced incomplete block designs with block size of 7, 8 or 9

Author keywords

BIBD; Group divisible design; RBIBD

Indexed keywords


EID: 0039436485     PISSN: 03817032     EISSN: 28175204     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (8)

References (47)
  • 2
    • 0002454159 scopus 로고    scopus 로고
    • On the existence of BIBDs with λ = 1 and 6 ≤ k ≤ 10
    • R.J.R. Abel, On the existence of BIBDs with λ = 1 and 6 ≤ k ≤ 10, J. Combin. Des. 4 (1996), 27-50.
    • (1996) J. Combin. Des. , vol.4 , pp. 27-50
    • Abel, R.J.R.1
  • 3
    • 0038890827 scopus 로고    scopus 로고
    • Some new BIBDs with block size 7
    • R.J.R. Abel, Some new BIBDs with block size 7. J. Combin. Des. 8 (2000), 146-150.
    • (2000) J. Combin. Des. , vol.8 , pp. 146-150
    • Abel, R.J.R.1
  • 4
  • 6
    • 0040027967 scopus 로고    scopus 로고
    • Resolvable and near resolvable designs
    • (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL
    • R.J.R. Abel and S.C. Furino, Resolvable and near resolvable designs, in: The CRC Handbook of Combinatorial Designs, (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL (1996), 87-94.
    • (1996) The CRC Handbook of Combinatorial Designs , pp. 87-94
    • Abel, R.J.R.1    Furino, S.C.2
  • 7
    • 0037835354 scopus 로고    scopus 로고
    • BIBDs with small block size
    • (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL
    • R.J.R. Abel and M. Greig, BIBDs with small block size, in: The CRC Handbook of Combinatorial Designs, (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL (1996), 41-47.
    • (1996) The CRC Handbook of Combinatorial Designs , pp. 41-47
    • Abel, R.J.R.1    Greig, M.2
  • 8
    • 0040075327 scopus 로고    scopus 로고
    • Balanced incomplete block designs with block size 7
    • R.J.R. Abel and M. Greig, Balanced incomplete block designs with block size 7, Des. Codes Cryptogr. 13 (1998), 5-30.
    • (1998) Des. Codes Cryptogr. , vol.13 , pp. 5-30
    • Abel, R.J.R.1    Greig, M.2
  • 10
  • 11
    • 0040668877 scopus 로고
    • Pairwise balanced designs with prime power block sizes exceeding 7
    • F.E. Bennett, Pairwise balanced designs with prime power block sizes exceeding 7, Ann. Discrete Math. 34 (1987), 43-64.
    • (1987) Ann. Discrete Math. , vol.34 , pp. 43-64
    • Bennett, F.E.1
  • 13
    • 0003723775 scopus 로고
    • Cambridge University Press, Cambridge UK (there is a second (1999) edition)
    • T. Beth, D. Jungnickel and H. Lenz, Design Theory, Cambridge University Press, Cambridge UK (1993); (there is a second (1999) edition).
    • (1993) Design Theory
    • Beth, T.1    Jungnickel, D.2    Lenz, H.3
  • 14
    • 0040075253 scopus 로고
    • On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements
    • R.C. Bose, On the application of finite projective geometry for deriving a certain series of balanced Kirkman arrangements, Calcutta Math. Soc. Golden Jubilee Commemoration Volume, Part II (1958 1959), 341-356.
    • (1958) Calcutta Math. Soc. Golden Jubilee Commemoration Volume , Issue.2 PART , pp. 341-356
    • Bose, R.C.1
  • 16
    • 0347068437 scopus 로고
    • A series of separable designs with application to pairwise orthogonal latin squares
    • Math. Centrum, Amsterdam (1979)
    • A.E. Brouwer, A series of separable designs with application to pairwise orthogonal latin squares, European J. Combin. 1 (1980), 39-41. Math. Centrum, Amsterdam (1979).
    • (1980) European J. Combin. , vol.1 , pp. 39-41
    • Brouwer, A.E.1
  • 17
    • 0002126293 scopus 로고
    • Group divisible designs with block-size four
    • A.E. Brouwer, A. Schrijver and H. Hanani, Group divisible designs with block-size four, Discrete Math. 20 (1977), 1-10.
    • (1977) Discrete Math. , vol.20 , pp. 1-10
    • Brouwer, A.E.1    Schrijver, A.2    Hanani, H.3
  • 18
    • 0000154250 scopus 로고
    • More mutually orthogonal latin squares
    • A.E. Brouwer and G. H. J. van Rees, More mutually orthogonal latin squares, Discrete Math. 39 (1982), 263-281.
    • (1982) Discrete Math. , vol.39 , pp. 263-281
    • Brouwer, A.E.1    Van Rees, G.H.J.2
  • 19
    • 0007123935 scopus 로고
    • A powerful method of constructing difference families and optical orthogonal codes
    • M. Buratti, A powerful method of constructing difference families and optical orthogonal codes, Des. Codes Cryptogr. 5 (1995), 13-25.
    • (1995) Des. Codes Cryptogr. , vol.5 , pp. 13-25
    • Buratti, M.1
  • 20
    • 0041125739 scopus 로고    scopus 로고
    • G-invariantly resolvable Steiner 2-designs which are 1-rotational over G
    • M. Buratti and F. Zuanni, G-invariantly resolvable Steiner 2-designs which are 1-rotational over G, Bull. Belg. Math. Soc. Simon Stevin 5 (1998), 221-235.
    • (1998) Bull. Belg. Math. Soc. Simon Stevin , vol.5 , pp. 221-235
    • Buratti, M.1    Zuanni, F.2
  • 22
    • 0000641964 scopus 로고
    • Some maximal arcs in finite projective planes
    • R.H.F. Denniston, Some maximal arcs in finite projective planes, J. Combin. Theory 6 (1969), 317-319.
    • (1969) J. Combin. Theory , vol.6 , pp. 317-319
    • Denniston, R.H.F.1
  • 23
    • 85168557009 scopus 로고
    • A few more BIBDs with k = 8 or 9
    • B. Du, A few more BIBDs with k = 8 or 9, Australas. J. Combin. 10 (1994), 245-249.
    • (1994) Australas. J. Combin. , vol.10 , pp. 245-249
    • Du, B.1
  • 25
    • 0007025719 scopus 로고
    • Some balanced incomplete block design constructions
    • M. Greig, Some balanced incomplete block design constructions, Congr. Numer. 77 (1990), 121-134.
    • (1990) Congr. Numer. , vol.77 , pp. 121-134
    • Greig, M.1
  • 26
    • 0040668875 scopus 로고    scopus 로고
    • Some group divisible design constructions
    • M. Greig, Some group divisible design constructions. J. Combin. Math. Combin. Comput. 27 (1998) 33-52,
    • (1998) J. Combin. Math. Combin. Comput. , vol.27 , pp. 33-52
    • Greig, M.1
  • 27
    • 0040075250 scopus 로고    scopus 로고
    • Designs from projective planes, and PBD bases
    • M. Greig, Designs from projective planes, and PBD bases, J. Combin. Des. 7 (1999), 341-374.
    • (1999) J. Combin. Des. , vol.7 , pp. 341-374
    • Greig, M.1
  • 28
    • 0040075249 scopus 로고    scopus 로고
    • Resolvable balanced incomplete block designs with a block size of 8
    • M. Greig and R.J.R. Abel, Resolvable balanced incomplete block designs with a block size of 8, Des. Codes Cryptogr. 11 (1997), 123-140.
    • (1997) Des. Codes Cryptogr. , vol.11 , pp. 123-140
    • Greig, M.1    Abel, R.J.R.2
  • 30
    • 49549139524 scopus 로고
    • Balanced incomplete block designs and related designs
    • H. Hanani, Balanced incomplete block designs and related designs, Discrete Math. 11 (1975), 255-369.
    • (1975) Discrete Math. , vol.11 , pp. 255-369
    • Hanani, H.1
  • 31
    • 0039483525 scopus 로고
    • BIBD's with block-size seven
    • H. Hanani, BIBD's with block-size seven, Discrete Math. 77 (1989), 89-96.
    • (1989) Discrete Math. , vol.77 , pp. 89-96
    • Hanani, H.1
  • 32
    • 0003723778 scopus 로고
    • Cambridge University Press, Cambridge UK
    • D.R. Hughes and F.C. Piper, Design Theory, Cambridge University Press, Cambridge UK (1985).
    • (1985) Design Theory
    • Hughes, D.R.1    Piper, F.C.2
  • 35
    • 0031073396 scopus 로고    scopus 로고
    • Pairwise balanced designs with block sizes 8, 9 and 10
    • A.C.H. Ling and C.J. Colbourn, Pairwise balanced designs with block sizes 8, 9 and 10, J. Combin. Theory Ser. A 77 (1997), 228-245.
    • (1997) J. Combin. Theory Ser. A , vol.77 , pp. 228-245
    • Ling, A.C.H.1    Colbourn, C.J.2
  • 37
    • 0039483524 scopus 로고    scopus 로고
    • A class of block designs having the same parameters as the design of points and lines in a protective 3-space
    • P. Lorimer, A class of block designs having the same parameters as the design of points and lines in a protective 3-space, Lecture Notes in Math. 403 73-78.
    • Lecture Notes in Math. , vol.403 , pp. 73-78
    • Lorimer, P.1
  • 38
    • 0038890815 scopus 로고
    • Two new block designs
    • W.H. Mills, Two new block designs, Utilitas Math. 7 (1975), 73-75.
    • (1975) Utilitas Math. , vol.7 , pp. 73-75
    • Mills, W.H.1
  • 39
    • 27844479584 scopus 로고
    • The construction of balanced incomplete block designs with λ = 1
    • University of Manitoba, Winnipeg MAN
    • W.H. Mills, The construction of balanced incomplete block designs with λ = 1, Proc. Seventh Manitoba Conf. on Numerical Mathematics and Computing, University of Manitoba, Winnipeg MAN (1977), 131-148.
    • (1977) Proc. Seventh Manitoba Conf. on Numerical Mathematics and Computing , pp. 131-148
    • Mills, W.H.1
  • 41
    • 0037814323 scopus 로고    scopus 로고
    • PBDs: Recursive constructions
    • (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL
    • R.C. Mullin and H-D.O.F. Gronau, PBDs: recursive constructions, in: The CRC Handbook of Combinatorial Designs, (C.J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL (1996), 193-203.
    • (1996) The CRC Handbook of Combinatorial Designs , pp. 193-203
    • Mullin, R.C.1    Gronau, H.-D.O.F.2
  • 42
    • 0038890812 scopus 로고    scopus 로고
    • PBDs, frames and resolvability
    • (C. J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL
    • R.C. Mullin and H-D.O.F. Gronau, PBDs, frames and resolvability, in: The CRC Handbook of Combinatorial, Designs, (C. J. Colbourn and J.H. Dinitz, eds.), CRC Press, Boca Raton FL (1996), 224-226.
    • (1996) The CRC Handbook of Combinatorial, Designs , pp. 224-226
    • Mullin, R.C.1    Gronau, H.-D.O.F.2
  • 44
    • 0040668871 scopus 로고
    • A method of construction of resolvable BIBD
    • E. Seiden, A method of construction of resolvable BIBD, Sankhyā Ser. A 25 (1963), 393-394.
    • (1963) Sankhyā Ser. A , vol.25 , pp. 393-394
    • Seiden, E.1
  • 45
    • 0002921967 scopus 로고
    • Cyclotomy and difference families in elementary abelian groups
    • R.M. Wilson, Cyclotomy and difference families in elementary abelian groups, J. Number Theory 4 (1972), 17-47.
    • (1972) J. Number Theory , vol.4 , pp. 17-47
    • Wilson, R.M.1
  • 46
    • 0000610109 scopus 로고
    • Concerning the number of mutually orthogonal latin squares
    • R.M. Wilson, Concerning the number of mutually orthogonal latin squares, Discrete Math. 9 (1974), 181-198.
    • (1974) Discrete Math. , vol.9 , pp. 181-198
    • Wilson, R.M.1
  • 47
    • 38249025080 scopus 로고
    • Some new matrices-minus-diagonal and MOLS
    • M. Wojtas, Some new matrices-minus-diagonal and MOLS, Discrete Math. 76 (1989), 291-292.
    • (1989) Discrete Math. , vol.76 , pp. 291-292
    • Wojtas, M.1


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