  We study the error detection problem in $ q $-ary asymmetric channels wherein
every input symbol $ x_i $ is mapped to an output symbol $ y_i $ satisfying $
y_i \geq x_i $. A general setting is assumed where the noise vectors are
(potentially) restricted in: 1) the amplitude, $ y_i - x_i \leq a $, 2) the
Hamming weight, $ \sum_{i=1}^n 1_{\{y_i \neq x_i\}} \leq h $, and 3) the total
weight, $ \sum_{i=1}^n (y_i - x_i) \leq t $. Optimal codes detecting these
types of errors are described for certain sets of parameters $ a, h, t $, both
in the standard and in the cyclic ($ \operatorname{mod}\, q $) version of the
problem. It is also demonstrated that these codes are optimal in the large
alphabet limit for every $ a, h, t $ and every block-length $ n $.
