ﻻ يوجد ملخص باللغة العربية
We give a characterization of all matrices $A,B,C in mathbb{F}_{2}^{m times m}$ which generate a $(0,m,3)$-net in base $2$ and a characterization of all matrices $B,Cinmathbb{F}_{2}^{mathbb{N}timesmathbb{N}}$ which generate a $(0,2)$-sequence in base $2$.
We discuss properties of integers in base 3/2. We also introduce many new sequences related to base 3/2. Some sequences discuss patterns related to integers in base 3/2. Other sequence are analogues of famous base-10 sequences: we discuss powers of 3
We delve into the connection between base $frac{3}{2}$ and the greedy partition of non-negative integers into 3-free sequences. Specifically, we find a fractal structure on strings written with digits 0, 1, and 2. We use this structure to prove that
Digital nets (in base $2$) are the subsets of $[0,1]^d$ that contain the expected number of points in every not-too-small dyadic box. We construct sets that contain almost the expected number of points in every such box, but which are exponentially s
We discuss two different systems of number representations that both can be called base 3/2. We explain how they are connected. Unlike classical fractional extension, these two systems provide a finite representation for integers. We also discuss a c
Dick proved that all order $2$ digital nets satisfy optimal upper bounds of the $L_2$-discrepancy. We give an alternative proof for this fact using Haar bases. Furthermore, we prove that all digital nets satisfy optimal upper bounds of the $S_{p,q}^r