Duals of Partially Balanced Incomplete Block Designs and some Nonexistence Theorems

Abstract

In this note, we give simpler proofs of results obtained, regarding the necessary conditions for existence of certain unsymmetrical PBIB designs having group divisible, triangular and $L_i$ association schemes, in [5]. We also give simpler proofs of the necessary conditions for the existence of affine $\alpha$-resolvable $GD(m, n), T(n), L_i(s)$ and BIB designs obtained in [6]. We follow the notation of these two papers throughout this note. We finally obtain necessary conditions for the dual of a design $D$, to be a specified design $E$.