NAME

pds.db - small database with planar difference set samples

VERSION

This is version 2.0 of the database, created on May 9, 2021.

DESCRIPTION

This file is the default database distributed with the Perl 5 module Math::DifferenceSet::Planar.

It contains 604 cyclic planar difference sets with orders ranging from 2 to 4096. The sets are chosen minimal by lexicographic ordering with priority on small over large elements, so that {0, 1, 3, 9} ranks before {0, 1, 4, 6}. It also contains planar difference set space data for the same range of orders. The radices are chosen with a greedy algorithm and not optimized for symmetry.

FILE FORMAT

SQLite 3.x database.

SCHEMA

  CREATE TABLE difference_set (
    order_      integer NOT NULL PRIMARY KEY,
    base        integer NOT NULL,
    exponent    integer NOT NULL,
    modulus     integer NOT NULL,
    n_planes    integer NOT NULL,
    deltas      blob    NOT NULL
  );

  CREATE TABLE difference_set_space (
    order_      integer NOT NULL PRIMARY KEY,
    mul_radix   integer NOT NULL,
    mul_depth   integer NOT NULL,
    rot_radices blob    NOT NULL,
    rot_depths  blob    NOT NULL
  );

DATA REPRESENTATION

If D = { d_1, d_2, ..., d_k } (mod m) is a canonical cyclic planar difference set of order k - 1 with d_1 ≡ 0 and d_2 ≡ 1 (mod m), deltas is a sequence of k - 2 numeric values packed in 'w*' format, calculated as differences of consecutive residue values of D starting with d_3 - d_2. The difference of the smallest two values in a canonical set is always 1 and thus not important to store.

If a multiplier set of the form {b^k | 0 ≤ k < e} with a radix b and depth e, and a rotator base of the form {r_1^j_1·r_2^j_2·...·r_n^j_n | 0 ≤ j_k < e_k, 1 ≤ k ≤ n} with n radices r_k and n depths e_k describe the multiplicative space of difference set planes of a given order, rot_radices and rot_depths are vectors of rotation radices and depths packed in 'w*' format.

PROVIDER

Martin Becker, <becker-cpan-mp at cozap.com>

COPYRIGHT AND LICENSE

Copyright (c) 2019-2022 by Martin Becker, Blaubeuren.

This library is free software; you can distribute it and/or modify it under the terms of the Artistic License 2.0 (see the LICENSE file).

The contents of this database are mathematically defined entities. The provider believes mathematical constants not to be proprietary or subject to copyright legislation, although the software used to calculate them and the accompanying documentation certainly are.