A Family of Binary Threshold Sequences Constructed by Using the Multiplicative Inverse

We point out that a family of pseudorandom binary lattices, which were constructed by using the multiplicative inverse, can be generated as binary threshold sequences. Hence we can estimate the well-distribution measure and the correlation measure of order l of the binary lattices in terms of discrepancy bounds on corresponding pseudorandom numbers in the interval [0, 1). We also consider the modified well-distribution measure and the modified correlation measure of order l, which were introduced by Sarkozy and Winterhof, for the binary lattices.

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