The nonexistence of (18,3,18,6) relative difference sets

Document Type

Conference Proceeding

Publication Date



It is known that relative difference sets with parameters (18,3,18,6) in a group of order 54 with normal subgroup N of order 3 do not exist in any abelian group of order 54. In this paper, using the recent classification of all generalized Hadamard matrices of order 18 over a group of order 3 [5], we show that such relative difference sets do not exist in any non-abelian group of order 54 as well. Our results are validated computationally using the computer algebra system Magma.

Publisher's Statement

Copyright Springer International Publishing Switzerland 2014. Publisher’s version of record: https://doi.org/10.1007/978-3-319-12325-7_13

Publication Title

Sequences and Their Applications - SETA 2014