Circuits and efficiency in incomplete block designs

Abstract

This paper explains why numbers of circuits in the variety concurrence graph of a design provide an attractive measure of its efficiency. It is conjectured that the search for designs with an optimal value of the harmonic mean efficiency factor can be restricted to those with minimal numbers of circuits of shorter lengths. This conjecture is seen to be highly plausible, to be a natural generalization of a conjecture that is already widely accepted and to offer significant savings in the construction of efficient designs.