# An extension of the digital method based on $b$-adic integers

## TL;DR

This paper extends digital sequence methods by integrating $b$-adic integers, resulting in new constructions with finite row-length generating matrices and improved distribution properties.

## Contribution

It introduces a hybrid digital-$b$-adic method with finite row-length matrices, connecting classical digital sequences to new, better-distributed constructions.

## Key findings

- New constructions with favorable $t, oldsymbol{T}$ and discrepancy measures
- Relations established between classical and extended digital methods
- Examples demonstrating improved uniform distribution properties

## Abstract

We introduce a hybridization of digital sequences with uniformly distributed sequences in the domain of $b$-adic integers, $\mathbb Z_{b}, b\in\mathbb N\setminus\{1\}$, by using such sequences as input for generating matrices. The generating matrices are then naturally required to have finite row-lengths. We exhibit some relations of the `classical' digital method to our extended version, and also give several examples of new constructions with their respective quality assessments in terms of $t,\mathbf T$ and discrepancy.