“…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.…”
Section: ' "Ttt-r) ' =(-1)'-'a'-'n (Noting That No=b N~--r N~=~mentioning
confidence: 92%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…
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].
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].
“…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.…”
Section: ' "Ttt-r) ' =(-1)'-'a'-'n (Noting That No=b N~--r N~=~mentioning
confidence: 92%
“…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.…”
Section: Introductionmentioning
confidence: 99%
“…
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].
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].
“…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.…”
Section: R A-designs With Mutually Balanced Nested Subdesignsmentioning
confidence: 99%
“…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 , . .…”
Some constructions of balanced arrays of strength two are provided by use of rectangular designs, group divisible designs, and nested balanced incomplete block designs. Some series of such arrays are also presented as well as orthogonal arrays, with illustrations.
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