Super-simple balanced incomplete block designs with block size 4 and index 5

In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super-simple designs are also useful in other constructions, such as superimposed codes and perfect hash families etc. The existence of super-simple (v,4,λ)(v,4,λ)-BIBDs have been determined for λ=2,3,4λ=2,3,4 and 6. When λ=5λ=5, the necessary conditions of such a design are that v≡1,4(mod12) and v≥13v≥13. In this paper, we show that there exists a super-simple (v,4,5)(v,4,5)-BIBD for each v≡1,4(mod12) and v≥13v≥13.