Chemical balance weighing designs under the restriction on the number of objects placed on the pans

The paper studies the problem of estimation of the weights of p objects in n weighings using a chemical balance weighing design under the restriction k(1) + k(2) < p, where k(1) and k(2) represent the number of objects placed on the right and left pans, respectively. The incidence matrices of balanced bipartite block designs are used to construct chemical balance weighing designs. The condition for estimates of weights to be uncorrelated is given.