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 . 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 . 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 $E$.
Damaraju Raghavarao. "Duals of Partially Balanced Incomplete Block Designs and some Nonexistence Theorems." Ann. Math. Statist. 37 (4) 1048 - 1052, August, 1966. https://doi.org/10.1214/aoms/1177699387