Abstract: Let G be a group of order 4p⁴ with Dihedral image D_4p², by investigating the intersection numbers, it is concluded that there is no Menon difference set in G if p≥5 (where p is a prime).

Key words: difference sets, intersection numbers, complete cyclic basis

摘要： 设G是具有二面体群同态象D_4p²的4p⁴阶群，通过考察其相交数得到如下结论：当p是素数且p≥5时，G上的差集不存在。

关键词: 差集, 相交数, 完全循环基