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. © 2008 Elsevier B.V. All rights reserved.