On accuracy of estimation of the number of steps for the algorithm for construction of scaling function on local fields

In this paper we discuss a problem of accuracy of estimation of the number of steps for the algorithm for construction of orthogonal scaling function which generates multiresolution analisys on local fields of positive characteristic. The resulting function is a step function with a compact support. The number of steps in the algorithm is closely related to the support of the Fourier transformation of the scaling function. Thus the estimate for number of steps is not only of computational interest. The upper estimate for this number was already known. In this work the accurate number of steps is found. It appeares to be equal to the previously known upper estimate.