On theλ-Design Conjecture

Aλ-design is a family ofvsubsets (blocks) of av-set such that any two distinct blocks intersect inλpoints and not all blocks have the same cardinality. Ryserʹs and Woodallʹsλ-design conjecture states that eachλ-design can be obtained from a symmetric design by complementing with respect to a fixed block. We prove this conjecture forv=p+1, 2p+1, 3p+1, wherepis prime.