  In this paper we study the non-existence problem of (nearly) perfect (almost)
$m$-ary sequences via their connection to (near) Butson-Hadamard (BH) matrices
and (near) conference matrices. Firstly, we apply a result on vanishing sums of
roots of unity and a result of Brock on the unsolvability of certain equations
over a cyclotomic number field to derive non-existence results for near BH
matrices and near conference matrices. Secondly, we refine the idea of Brock in
the case of cyclotomic number fields whose ring of integers is not a principal
ideal domains and get many new non-existence results.
