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Optimal chemical balance weighing designs for $$v+1$$ objects. (English) Zbl 1248.62128
Summary: The paper studies the estimation problem of individual weights of objects using a chemical balance weighing design under the restriction on the number times in which each object is weighed. Conditions under which the existence of an optimum chemical balance weighing design for $$p = v$$ objects implies the existence of an optimum chemical balance weighing design for $$p = v + 1$$ objects are given. The existence of an optimum chemical balance weighing design for $$p = v + 1$$ objects implies the existence of an optimum chemical balance weighing design for each $$p < v + 1$$. A new construction method for optimum chemical balance weighing designs for $$p = v + 1$$ objects is given. It uses the incidence matrices of ternary balanced block designs for $$v$$ treatments.
##### MSC:
 62K05 Optimal statistical designs 62K10 Statistical block designs
##### Keywords:
ternary balanced block designs
Full Text:
##### References:
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