Optimum chemical balance weighing designs for v+1 objects
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. The new construction method for optimum chemical balance weighing design for p = v + 1 objects is given. It uses the incidence matrices of ternary balanced block designs for v treatments.
chemical balance weighing design ternary balanced block design