Super-simple group divisible designs with block size 4 and index λ = 7,8

Abstract

A design is said to be super-simple if the intersection of any two blocks has at most two elements. In statistical planning of experiments, super-simple designs provide samples with intersection as small as possible. Super-simple group divisible designs are also useful for constructing other types of super-simple designs, which can be applied to codes and designs. In this article, we investigate the existence of a super-simple (4,λ)-GDD of group type gu, where λ=7,8, and show that such a design exists if and only if u≥4, g(u−2)≥2λ, g(u−1)≡0(mod3) and λu(u−1)g2≡0(mod12).