A hypothesis testing problem is considered for the hypothesis that the process \(\{x_ t:\) \(t\in [0,T]\}\) has “white noise” \[ dx_ t=\epsilon dw_ t,\quad \epsilon >0, \] and alternative that \[ dx_ t=s_ t dt+\epsilon dw_ t. \] Here \(\{w_ t\}\) is a standard Wiener process and \(s_ t\in S\subset L_ 2([0,T])\). The set S is supposed to consist of a finite number N(\(\epsilon\)) of orthonormal signals. The authors evaluate the order of growth of N(\(\epsilon\)) when \(\epsilon\to 0\), providing some decrease of the critical first and second kind errors.