A necessary condition for the $\alpha$-resolvability of an incomplete block design is obtained. Further, a necessary and sufficient condition for an $\alpha$-resolvable incomplete block design to be affine $\alpha$-resolvable is obtained in terms of the largest characteristic root of $NN'$ other than $rk$, where $N$ is the incidence matrix of the design.
"On $\alpha$-Resolvability and Affine $\alpha$-Resolvability of Incomplete Block Designs." Ann. Statist. 6 (2) 468 - 471, March, 1978. https://doi.org/10.1214/aos/1176344138