Super-simple balanced incomplete block designs with block size 4 and index 8

Abstract

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, 9. In this paper, we investigate the existence of a super-simple(v, 4, 8)-BIBD and show that such a design exists if and only if v = 1(mod 3) and v ≥ 19. Applications of the results in coding theory are also mentioned.