Block Design - Resolvable 2-designs

Resolvable 2-designs

A resolvable 2-design is a BIBD whose blocks can be partitioned into sets (called parallel classes), each of which forms a partition of the point set of the BIBD. The set of parallel classes is called a resolution of the design.

If a 2-(v,k,λ) resolvable design has c parallel classes, then b ≥ v + c - 1.

Consequently, a symmetric design can not have a non-trivial (more than one parallel class) resolution..

Archetypical resolvable 2-designs are the finite affine planes. A solution of the famous 15 schoolgirl problem is a resolution of a 2-(15,3,1) design.