Abstract Super-simple designs are used in other constructions, such as coverings, superimposed codes and perfect hash families etc. The existence of super-simple ( v , 4 , λ ) -BIBDs has been determined for λ = 2 , 3 , 4 , 5 , 6 and 9. When λ = 7 , the necessary conditions of such a design are that v ≡ 1 , 4 (mod 12) and v ≥ 16 . In this paper, we show that these necessary conditions are sufficient.

中文翻译：

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具有块大小 4 和索引 7 的超简单 BIBD

摘要 超简单设计用于其他结构，如覆盖、叠加码和完美散列族等。 超简单 ( v , 4 , λ ) -BIBD 的存在性已确定为 λ = 2 , 3 , 4 , 5、6 和 9。当 λ = 7 时，这种设计的必要条件是 v ≡ 1 , 4 (mod 12) 和 v ≥ 16 。在本文中，我们证明这些必要条件是充分的。