Three symbol partially balanced arrays

Abstract

SummaryTwo methods of construction of partially balanced arrays of strength two and three are presented.

Note on the construction of partially balanced arrays

“…The special cases of this theorem when t=2 and 3 are shown by Dey, Kulshreshtha and Saha [4]. Generally, if n* in (2.1) may be defined by n~+n*=l-1, then there exists an /-symbol PB array.…”

“…If, for every trowed submatrix of A, the s t t • 1 matrices X occur as columns ~1~.~-.-~, times, then the matrix A is called an s-symbol Partially Balanced (PB) array of strength t with m assemblies, n constraints (or factors) and parameters /~ .... ...~, which was first introduced by Chakravarti [2] as a substitute for the orthogonal array, both serving the purpose of fractional replicates of factorial experiments. Recently, Dey, Kulshreshtha and Saha [4] have given a method of constructing three-symbol PB arrays of strength two and three. In this note, it is shown that three-symbol and four-symbol PB arrays of strength t are constructed by using their method.…”

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SummaryThe p-symbol partially balanced arrays of strength t, where p=3 and 4, are given by a method due to A. Dey, A. C. Kulshreshtha and G. M. Saha [4].

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Balanced arrays of strength two and nested (r, λ)‐designs

“…It is well-known that the existence of an (r,A)-design ( V , B ) is equivalent to the existence of a BA(v,b,2,2) with indices p I 1 = A, pol = r -A and poo = b -2r + A, where b is the number of blocks of B . In the case of more than 2 symbols, Dey, Kulshreshtha, and Saha [5] have shown a construction of balanced arrays with 3 symbols from BIBD's. Kageyama 181 has improved the result for s 2 3.…”

“…From Corollary 3.2, we construct a BA(v,26,3,2) with indices p12 = 0, p l l = p 2 2 = A, pol = po2 = r -A and pou = 2(b -2r + A). This is the case of Dey, Kulshreshtha, and Saha [5]. If we partition each block B into B, + , 4 , . .…”