Ternary 1-designs (V,B;ρ1,pρ2,R; K)

Abstract

It is well known that the necessary conditions V R = BK and B ≤ (^V_K) are sufficient for the existence of a simple binary 1-design with parameters V, R, K. In the present note this result is generalized for some classes of simple ternary 1-designs including the cases when block size is 3 or block size is 4. Several necessary conditions are obtained for arbitrary block sizes. Necessary and sufficient conditions are proven for the existence of ternary 1-designs in general, if repetition of blocks is allowed.