Some new equireplicate balanced block designs

May 1989

Statistics & Probability Letters 8 (1989) 89 North-Holland

SOME NEW EQUIREPLICATE

BALANCED

BLOCK DESIGNS

Kishore SINHA Department

of Statistics, Birsa Agricultural University, Ronchi-834006, India

Received September 1987 Revised August 1988

Abstract:

Some new equireplicate balanced block designs in the range r < 30 are listed.

Keywords:

bahmced block design, PBIB design.

Balanced block designs

References Aganval, G.G. and S. Kumar (1984) On a class of variance balanced designs associated with GD designs, Calcutta Stotist. Asses. Bull. 33, 187-190. Clatworthy, W.H. (1973), Tables of two-associate-class partially balanced designs (National Bureau of Standards, Washington, D.C.). Gupta, S.C. and B. Jones (1983). Equireplicate balanced block designs with unequal block sires, Biometriko 70 (2), 433-440. John, P.W.M. (1985), Constructing balanced designs from triangular designs, Statist. Probab. L&t. 3, 19-20. Jones, B., K. Sinha and S. Kageyama (1987) Further equireplicate balanced block designs with unequal block sizes, Utilitas Mathematics 32, 5-10. Sinha, K. (1988), Equireplicate balanced block designs from BIB designs, J. Indian Sot. Agril. Statist., to appear. Sinha, K. and B. Jones (1987) Further equirephcate balanced block designs with unequal block sizes, Statist. Protxrb. Lett. 6, 141-142.

Equireplicate balanced block designs have been enumerated by AgarwaI and Kumar (1984), Gupta and Jones (1983), John (1985), Jones, Sinha and Kageyama (1987), Sinha (1988), and Sinha and Jones (1987). The designs have been obtained by combining suitable PBIB designs. We list some new designs obtained by combining three PBIB designs. p( m, n) stands for repeating p times the m groups, each of size n, as blocks. The references to design numbers are to Clatworthy (1973).

Acknowledgement The author is thankful to the referee for his remarks. Table 1 Equireplicate balanced block designs with r d 30. smial no.

V

r

k,

kz

k,

b,

bz

b,

w

1OOE

source

1 2 3 4 5 6 7 8 9 10 11

8 8 8 9 10 12 16 16 16 21 21

16 18 26 23 25 18 27 28 30 17 22

2 2 2 2 2 2 3 2 2 2 2

3 3 3 3 4 3 4 4 3 3 3

4 _ 4 _ 4 4 6 6

12 36 20 54 105 54 96 192 72 105 105

24 24 24 33 10 12 36 16 48 35 70

8 _ 24 _ _ 18 _ 48 7 7

312 3/2 512 5/3 312 1 5/4 1 312 l/2 213

75.0 66.7 76.9 57.7 60.0 66.7 74.1 57.1 80.0 61.8 63.6

3R54 + SR36 + 3(4,2) 3R54 + R29 + 3(4,2) 3(R54 + SR36) + 5(4,2) 2(SR23 + R34) + 5(3,3) 2(Tl+ T28) + 3T2 2SR41+ R39 + 3(4,3) SR44 + 3186 + 5(4.4) LS3 + 2LS28 + 2LS4 LS4+ 3LS18 + 6LS28 T2O+T65+T8 T7+T65+T22

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0 1989, Elsevier Science Publishers B.V. (North-Holland)

89