关于单纯B[4,2;v]和B[m,3;v]的存在性

Existence of Simple B[4,2;v] and B[4,3;v]

一个B[k,λ;v]中,若不包含重复区组,则称为单纯的.本文证明了单纯B[4,2;v]和B[4,3;v]存在的充要条件分别是v≡1(mod3),v≠4和v≡0,1(mod 4),v≠4.

A B[k,λ;v]is called simple if it contains no repeated blocks.It isproved in this paper that the necessary conditions for the existence of a sim-ple B[4,λ;v]are also sufficient in the cases of λ=2 and 3.