Proof of a conjecture on semiregular relative difference sets in Zp2 × Zp2

In this article we show that there is no (p3, p, p3, p2)-difference set in Zp2 × Zp2 for all primes p > 3. This is an affirmative answer to a conjecture raised by S.L. Ma and B. Schmidt.

[1]  K. Williams,et al.  Gauss and Jacobi sums , 2021, Mathematical Surveys and Monographs.

[2]  Siu Lun Ma,et al.  On (pa, p, pa, pa−1)-relative difference sets , 1995, Des. Codes Cryptogr..

[3]  Y. Berkovich,et al.  Characters of Finite Groups. Part 1 , 1997 .

[4]  James A. Davis,et al.  A Unifying Construction for Difference Sets , 1997, J. Comb. Theory, Ser. A.

[5]  I︠a︡. G. Berkovich,et al.  Characters of finite groups , 1997 .

[6]  Siu Lun Ma,et al.  Relative (p a , p b , p a , p a-b -Difference Sets , 2000 .