On balanced complementation for regular t-wise balanced designs (Q1122581)

A regular t-wise design is a generalization of the notion of an (r,\(\lambda)\)-design to t-wise balance: It is a collection of blocks of a v-set V such that any s points \((s=0,...,t)\) are contained in a constant number \(\lambda_ s\) of blocks. Note that different block sizes are allowed. Generalizing a method due to \textit{S. A. Vanstone} for \(t=2\) [``A bound for \(v_ 0(r,\lambda)''\), Proc. 5th Southeast. Conf. Comb., Graph Theory, Comput.; Boca Raton 1974, 661-673 (1974; Zbl 0312.05015)], the authors give a construction method for regular t-wise balanced designs which consists in complementing all the blocks in a suitable subset of the block set. They also give some applications.