=encoding utf8

=head1 NAME

extra.db - additional database with planar difference set sample

=head1 VERSION

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

=head1 DESCRIPTION

This file is an additional sample database only used for testing.

It contains 1 cyclic planar difference set with order 11, together with
all metadata.  The set is chosen minimal by lexicographic ordering.

=head1 FILE FORMAT

SQLite 3.x database.

=head1 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
  );

=head1 DATA REPRESENTATION

If I<D = { d_1, d_2, ..., d_k } (mod m)> is a canonical cyclic
planar difference set of order I<k - 1> with I<d_1 E<8801> 0> and
I<d_2 E<8801> 1 (mod m)>, I<deltas> is a sequence of I<k - 2> numeric
values packed in C<'w*'> format, calculated as differences of consecutive
residue values of I<D> starting with I<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 I<{b^k | 0 E<8804> k E<lt> e}>
with a radix I<b> and depth I<e>, and a rotator base of the form
I<{r_1^j_1E<183>r_2E<183>j_2E<183>...E<183>r_n^j_n>
I<| 0 E<8804> j_k E<lt> d_k, 1 E<8804> k E<8804> n}>
with I<n> radices I<r_k> and I<n> depths I<d_k> describe the
multiplicative space of difference set planes of a given order,
I<rot_radices> and I<rot_depths> are vectors of rotation radices and
depths packed in C<'w*'> format.

=head1 PROVIDER

Martin Becker, E<lt>becker-cpan-mp I<at> cozap.comE<gt>

=head1 COPYRIGHT AND LICENSE

Copyright (c) 2019-2021 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.

=cut
