摘要
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types of super- simple designs which can be applied to codes and designs. In this article, the existence of a super-simple (5, 4)-GDD of group type gU is investigated and it is shown that such a design exists if and only if u ≥ 5, g(u - 2) ≥ 12, and u(u - 1)g^2≡ 0 (mod 5) with some possible exceptions.
In statistical planning of experiments, super-simple designs are the ones providing samples with maximum intersection as small as possible. Super- simple group divisible designs are useful in constructing other types of super- simple designs which can be applied to codes and designs. In this article, the existence of a super-simple (5, 4)-GDD of group type gU is investigated and it is shown that such a design exists if and only if u ≥ 5, g(u - 2) ≥ 12, and u(u - 1)g^2≡ 0 (mod 5) with some possible exceptions.
基金
Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant Nos. 11371121, 11371308, 11201114, 11301457).