nx - signifies Niederreiter/Xing construction
s.. - dimension = no. of matrices
m.. - log no. of points, precision, size of matrices
First entry : m
Second entry : s
Next s*m entries : row vectors of the first, second,..., s-th
matrix, encoded as decimal number.
The vector consists of the digits of the b-ary expansion of the number,
most significant bits corresponding to the initial coordinates of the
vector. (E.g. b = 2, m = 8: entry 11 <-> row vector [0 0 0 0 1 0 1 1] )
All files in one .tgz archive : nxsmats.tgz
For t-values look here .
Each column is one dimension, m increases with the row number
(m grows down, s across). Also a
transposed version is available as well as one
transposed (i.e. each row is one dimension) and
with propagation rules applied.
The above format is designed for calculating the t-value. For
calculating the actual points, the
file under this link is a tar-gzip
compressed collection of the above matrices for use with the
libseq-library of Ilja Friedel and Alexander Keller.
(ATTENTION: As Thomas Kollig thankfully pointed out, there had been
an error in the libseq-formatted files provided earlier: the intended
original matrices would have been like the entries in the files but
with 0 and 1 interchanged.)
Under this link you can get an example C++ program
(MS Windows version here)
implementing the generation of the points (not the matrices!)
(tested under Linux (g++) and Windows
(cygwin) ).
Two further HIGHDIMENSIONAL matrices in the libseq format:
base 16, dimension 63, matrix size 30, t at most 6 :
fkmat63b16
base 64, dimension 511, matrix size 32, t at most 28 :
fkmat511b64
(Note: the TABLE_LENGTH in `options.h' of `libseq' may have to be increased to
use this matrices!)
Please contact me at
Gottlieb.Pirsic@oeaw.ac.at if you need larger matrix sizes
( = more points = higher precision )
for any of the above dimensions/bases or any further clarification.
A KASH script
for generation of the matrices of the base 2 sequences in the above dimensions
is available under this link.
(Older version: here)
This file (prototypes) is for variable declaration
and
this file (ffdata) holds function field data - here
is where you may add further high rational place count function fields.
All three files (niedxing_v?.kash, prototypes, ffdata) are required to
exist in the same directory (e.g. your KASH directory) for the script to
run correctly.
After the script is loaded into the KASH system, type
A C++ program is available on demand, for s at most 16. (However, I still don't trust it fully yet, so preferrably please use the above KASH script... )