On Some Methods of Construction of Partially Balanced Arrays

“…Each of the sets of assemblies Sr(j) covered in the above enumeration constitutes a degenerate partially balanced array of full strength n as defined by I. M. Chakravarti [5], [6]. That the arrays are degenerate is a consequence of their being of full strength, since the only nondegenerate partially balanced array of full strength is necessarily all of factor space itself.…”

Section: Generation Of Sets Of Partially Balanced Arraysmentioning

confidence: 99%

Economical Second-Order Designs Based on Irregular Fractions of the 3 n Factorial

Hoke¹

1974

Technometrics

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“…It was shown by Chakravarti [10] that partially balanced arrays for 5 = 2 can be constructed from a X -n -v configuration. A X -/i -v configuration (or tactical configuration) of m elements is defined by Carmichael [9] as the configuration of m elements taken v at a time so that each subset of y. elements shall occur together in just X of the sets.…”

Section: Biliary Shs(m N) and Partially Balanced Arrays In Two Symbolsmentioning

confidence: 99%

On Some Strongly and Weakly Homogeneous Binary Search Systems

Manglik¹

1972

Journal of Cybernetics

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Given a non-empty set S and a system F of functions defined on 5, the object of search is to detect an unknown element x in S, by observing the values of a sequence of test-functions / in F at x till there is enough information to detect x. The basic concepts and definitions of search theory were developed by Re'nyi [16,17]. He defined various types of homogeneities for the system F and discussed the duration of the process of random search.Strongly homogeneous systems of order two in two symbols are found to be closely related to the incidence matrix of equireplicated pairwise balanced designs. Some new systems of this type have been constructed here by using the incidence of subsets of points and ra-flats of finite geometries. Properties of weakly homogeneous binary systems of order two have been studied, and some new systems constructed using association matrices and Hadamard matrices. Two series of search systems possessing an optimality property have been also constructed.

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On Some Methods of Construction of Partially Balanced Arrays

Cited by 42 publications

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Note on the construction of partially balanced arrays

Note on the construction of partially balanced arrays

Economical Second-Order Designs Based on Irregular Fractions of the 3 n Factorial

On Some Strongly and Weakly Homogeneous Binary Search Systems

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