Optimal chemical balance weighing designs for $v+1$ objects

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 $p < v + 1$. 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