Existence of affine \(\alpha\)-resolvable PBIB designs with some constructions (Q730700)

The authors employ number-theoretic means to investigate affine \(\alpha\)-resolvable partially balanced incomplete block (PBIB) designs with two associate classes, characterizing parameters in closed form, dealing with existence questions, and providing new methods of construction. Tables are provided for affine resolvable singular group divisible designs, for affine resolvable semi-regular group divisible designs, and for affine resolvable Latin-square designs, all with \(v\leq 100\) and \(r,k\leq 20\). Of these, existence is unknown in only six cases.