Super-simple balanced incomplete block designs with block size 5 and index 3

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 constructing codes and designs such as superimposed codes and perfect hash families. The existence of super-simple (v, 4, λ)BIBDs have been determined for λ = 2, 3, 4, 5, 6. In this paper, we investigate the existence of a supersimple (v, 4, 9)-BIBD and show that such a design exists if and only if v ≡ 0, 1 (mod 4) and v ≥ 20.