Generalized partially balanced incomplete block designs

Discrete Mathematics North-Holland

327

90 (1991) 327

Corrigendum To: Kishore Sinha, “Generalized partially balanced incomplete block designs”, Discrete Mathematics 67 (1987) 315-318. Received 10 August 1989 Revised 2 May 1990

The concept of generalized PBIB design is extended here as: A generalized PBIB design with m-associate classes is an arrangement of a set of v elements (treatments) into b subsets (blocks) such that the following conditions are fulfilled: (i) each element occurs in exactly r subsets, (ii) each subset contains exactly k (
The Theorems 3.1 and 3.2 in the article may easily be extended for the above definition. The examples of two generalized PBIB designs given there do not conform to the original definition, but conform to the extended definition with parameters as: (1) u = 15, b = 9, r = 3, k = 5, A1 = 2, & = 1, A, = 0, and, (2) v = 15 = b, r = 6 = k, A, = 1, A2= 2, A3= 3 and for both the designs: (i) for treatments: 0, 1,2,3,4,10,11,13: n, =2,

rl2 = 8,

(ii) for treatments: ni = 1,

n1 =O,

5, 6, 7, 8, 12, 14:

n2 = 10,

(iii) for treatment:

It3 = 4,

n3 = 3,

9:

n2 = 12,

n3 = 2.

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