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 ) -BIBDs have been determined for λ = 2 , 3 , 4 and 6. When λ = 5 , the necessary conditions of such a design are that v ≡ 1 , 4 ( mod 12 ) and v ≥ 13 . In this paper, we show that there exists a super-simple ( v , 4 , 5 ) -BIBD for each v ≡ 1 , 4 ( mod 12 ) and v ≥ 13 .