## Abstract

A balanced incomplete block design or BlBD is defined as an arrangement of v objects in b blocks, each block containing k objects all different, so that there are r blocks containing a given object and lambda blocks containing any two given objects.

In this note we shall extend a method of Sprott [2, 3] to obtain several new families of BIBD's. The method is based on the first Module Theorem of Bose [1] for pure differences.

We shall frequently be concerned with collections in which repeated elements are counted multiply, rather than with sets. If T_{1 }and T_{2} are two such collections then T_{1} & T_{2} will denote the result of adjoining the elements of T_{1} to T_{2}, with total multiplicities retained. We use the brackets, { }, to denote sets and square brackets, [ ], to denote collections of elements which may have repetitions. See [5] for results using these concepts.

## Publication Details

Jennifer Seberry Wallis, A note on BIBDS, Journal of Australian Mathematical Society, 16, (1973), 257-261.