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.
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