Super-simple balanced incomplete block designs with block size 4 and index 9

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 – 6 . In this paper, we investigate the existence of a super-simple ( v , 4 , 9 ) -BIBD and show that such a design exists if and only if v ≡ 0 , 1 ( mod 4 ) and v ⩾ 20 . Applications of the results to optical orthogonal codes are also mentioned.