# Frolov cubature points in $[0,1]^d$

The table at the bottom allows to download the Frolov cubature points for dimensions between 2 and 10 and points numbers up to 1.000.000.

• Each file contains approximately $N=2^{\text{level}}$ points.
• The text-files follow the format:

# Comments
{dimension} d
{number of points} N
{integration weight} w
{x_1} {x_2} ... {x_d}

C. Kacwin, J. Oettershagen, M. Ullrich and T. Ullrich. Numerical performance of optimized Frolov lattices in tensor product reproducing kernel Sobolev spaces. ArXiv e-prints, 2017. [pdf]

### Software examples

A zip archieve with all files for level 1..20 and dimension 2..10 can be downloaded here (about 1 GB).

lvl \ dim 2 3 4 5 6 7 8 9 10
1 @ @ @ @ @ @ @ @ @
2 @ @ @ @ @ @ @ @ @
3 @ @ @ @ @ @ @ @ @
4 @ @ @ @ @ @ @ @ @
5 @ @ @ @ @ @ @ @ @
6 @ @ @ @ @ @ @ @ @
7 @ @ @ @ @ @ @ @ @
8 @ @ @ @ @ @ @ @ @
9 @ @ @ @ @ @ @ @ @
10 @ @ @ @ @ @ @ @ @
11 @ @ @ @ @ @ @ @ @
12 @ @ @ @ @ @ @ @ @
13 @ @ @ @ @ @ @ @ @
14 @ @ @ @ @ @ @ @ @
15 @ @ @ @ @ @ @ @ @
16 @ @ @ @ @ @ @ @ @
17 @ @ @ @ @ @ @ @ @
18 @ @ @ @ @ @ @ @ @
19 @ @ @ @ @ @ @ @ @
20 @ @ @ @ @ @ @ @ @