An Addition Structure on Incidence Matrices of a \(BIB\) Design

Abstract

For a balanced incomplete block (BIB) design, the following problem is considered: Find \(s\) different incidence matrices of the BIB design such that (i) for \(1 \leq t \leq s-1\), sums of any \(t\) different incidence matrices yield BIB designs and (ii) the sum of all \(s\) different incidence matrices becomes a matrix all of whose elements are one. In this paper, we show general results and present four series of such BIB designs with examples of three other BIB designs.