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

الملخص EN

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.