Let \(n,r,m\in\mathbb N\), \(m\geq r\), \(W^{(r)}_{p}\) be the space of \(2\pi\)-periodic functions whose \((r - 1)\)th-order derivative is absolutely continuous on any segment and \(r\)th-order derivative belongs to \(L_p\), and \(S_{2n,m}\) be the space of \(2\pi\)-periodic splines of order \(m\) of minimal defect over the uniform partition \(k\pi/n\) (\(k\in\mathbb Z\)). The author constructs linear operators \(X_{n,r,m}:L_1\to S_{2n,m}\) such that
\[ \sup_{f\in W^{(r)}_{\infty}} \frac{\| f-X_{n,r,m}(f)\| _\infty}{\| f^{(r)}\| _\infty}= \sup_{f\in W^{(r)}_1} \frac{\| f-X_{n,r,m}(f)\| _1}{\| f^{(r)}\| _1}= \frac{K_r}{n^r}, \] where
\[ K_r= \dfrac4\pi\sum\limits_{l=0}^{\infty} \dfrac{(-1)^{l(r+1)}}{(2l+1)^{r+1}}. \]
The operators \(X_{n,r,m}\) are constructed using the interpolation of Bernoulli kernels. As is proved, the operators \(X_{n,r,m}\) converge to polynomial Akhiezer-Krein-Favard operators as \(m\to\infty\).