Discussiones Mathematicae Probability and Statistics 24(1) (2004) 41-58

ON A CHARACTERIZATION OF SYMMETRIC BALANCED INCOMPLETE BLOCK DESIGNS

R.N.  Mohan,

P.G. Department of Mathematics, Sir C.R.R. College
Eluru-534007, India

e-mail: vjwrnmohan@sancharnet.in

Sanpei Kageyama

Hiroshima University,
Higashi-Hiroshima 739-8524, Japan

e-mail: ksanpei@hiroshima-u.ac.jp

M.M. Nair

Sarathi Institute of Engineering and Technology
Nuzvid-521201, India

Abstract

All the symmetric balanced incomplete block (SBIB) designs have been characterized and a new generalized expression on parameters of SBIB designs has been obtained. The parameter b has been formulated in a different way which is denoted by bi, i = 1, 2, 3, associating with the types of the SBIB design Di. The parameters of all the designs obtained through this representation have been tabulated while corresponding them with the suitable formulae for the number ofblocks bi and the expression Si for the convenience of practical users for constructional methods of certain designs, which is the main theme of this paper.

Keywords: symmetric balanced incomplete block (SBIB) design.

2000 Mathematics Subject Classification: 05B05.

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Received 15 September 2003