Pairwise Balanced Design of Order 6n+4 and 2-Fold System of Order 3n+2. (27th December 2012) - Basu, Manjusri; Ghosh, Debabrata Kumar; Bagchi, Satya
Abstract : In the Steiner triple system, Bose (1939) constructed the 2 − ( v, 3, 1 ) design for v = 6 n + 3 and later on Skolem (1958) constructed the same for v = 6 n + 1 . In the literature we found a pairwise balanced design (PBD) for v = 6 n + 5 . We also found the 2-fold triple system of the orders 3 n and 3 n + 1 . In this paper, we construct a PBD for v = 6 n + 4 and a 2-fold system of the order 3 n + 2 . The second construction completes the 2-fold system for all n ∈ N .