Optimal weighing schemes

We study the problem of determining the masses of a set of weights, given one standard weight, based on comparing two disjoint subsets of those weights with approximately equal mass. The question is how to choose a weighing scheme, i.e., different pairs of subsets, such that the masses can be determined as accurately as possible within a given number of measurements. In this paper we discuss a new way of using the so-called STS method of comparing two approximately equal masses, and we will give optimal weighing schemes which turn out to outperform schemes that are currently used by national metrology institutes.