Classification of semiregular relative difference sets with gcd(λ, n)=1 attaining Turyn’s bound

• Main Authors: Leung, Ka Hin, Schmidt, Bernhard, Zhang, Tao
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2024
• Subjects: Mathematical Sciences; Exponent bound; Direct product difference sets
• Online Access: https://hdl.handle.net/10356/174655
• Institution: Nanyang Technological University

Suppose a (λn,n,λn,λ) relative difference set exists in an abelian group G=S×H, where |S|=λ, |H|=n2, gcd(λ,n)=1, and λ is self-conjugate modulo λn. Then λ is a square, say λ=u2, and exp(S) divides u by Turyn’s exponent bound. We classify all such relative difference sets with exp(S)=u. We also show...