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A note on construction of symmetrical PBIB designs

✍ Scribed by P.S. Gill

Publisher: Elsevier Science
Year: 1984
Tongue: English
Weight: 319 KB
Volume: 51
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90011-6

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✦ Synopsis

In this note initial block technique hzs been used for construction of some cl=s of

3-associate PBIB designs, known as rectangular desigus.

Let A = MX S be the Cartesian produd of M and S, where .M = (a~, a lr. . . , qn_3 is an additive group of order m and S = (0, I,. . . , s -1). I& a,l' denote a typical element of A. The rectangular association scheme for the MS symbols of A is defined as a scheme in which two symbols qj and uJ' are called first associates if i = i'; second associates if j = j'; and third associates otherwise.

We define a rectangular PBIB design (to be denoted by RIB) as an arrangement of the 312s sy&ols of A in b blocks each of size k (ems) such that (i) every symbo1 occuxs at most once in a block,

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