Publication Details

Jane di Paola, Jennifer Seberry Wallis and W. D. Wallis, A list of balanced incomplete block designs for r < 30, Proceedings of the Fourth Southeastern Conference on Combinatorics, Graph Theory and Computing, Congressus Numerantium, 8, (1973), 249-258.


A balanced incomplete block design consists of a set of v elements arranged into b k-element subsets called blocks such that each element occurs r times and each pair of elements appears in lambda distinct blocks. The numbers v,b,r,k,lambda are called the parameters of the design. A necessary condition that a design exist is that the parameters be integers satisfying:

(1) vr = bk

( 2) r(k-1) = lambda (v-1)