OBIBDs (Orthogonal Balanced Incomplete Block Designs)

New theorems for OBIBDs

• A construction where v is a prime number or prime power, of form 12t+7, k=3 and λ = 1. This is a generalisation of a well-known construction of Steiner Triple Systems, attributed to Netto.

  A Steiner Triple System (STS) is a BIBD with k = 3 and λ = 1.

• A generalisation of this to designs with k > 3 and λ = (k-1)/2.

  I have not seen the equivalent construction for BIBDs anywhere, but it is an instance of a well-known construction using groups (see BJL III.4.6).

• Further generalisations with λ < (k-1)/2

• Designs based on projective geometry.

• Designs based on generalisations from fields to rings.