Publication Details

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


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 T1 and T2 are two such collections then T1 & T2 will denote the result of adjoining the elements of T1 to T2, 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.