Pairwise Balanced Design of Order 6n+4 and 2-Fold System of Order 3n+2

Manjusri Basu, Debabrata Kumar Ghosh, Satya Bagchi
2012 ISRN Discrete Mathematics  
In the Steiner triple system, Bose (1939) constructed the 2−(v,3,1) design for v=6n+3 and later on Skolem (1958) constructed the same for v=6n+1. In the literature we found a pairwise balanced design (PBD) for v=6n+5. We also found the 2-fold triple system of the orders 3n and 3n+1. In this paper, we construct a PBD for v=6n+4 and a 2-fold system of the order 3n+2. The second construction completes the 2-fold system for all n∈N.
doi:10.5402/2012/251457 fatcat:uie2zwaumzakvnvg4yjr3rjwoy