On Irregularities of Distribution of Binary Sequences Relative to Arithmetic Progressions, II (Constructive Bounds)
, and | Jan 25, 2019
Published Online: Jan 25, 2019
Page range: 1 - 21
Received: Dec 20, 2016
Accepted: Nov 11, 2017
DOI: https://doi.org/10.2478/udt-2018-0008
Keywords
© 2018 Cécile Dartyge et al., published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.
In Part I of this paper we studied the irregularities of distribution of binary sequences relative to short arithmetic progressions. First we introduced a quantitative measure for this property. Then we studied the typical and minimal values of this measure for binary sequences of a given length. In this paper our goal is to give constructive bounds for these minimal values.