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r""" Catalog of designs
This module gathers all designs that can be reached through ``designs.<tab>``. Example with the Witt design on 24 points::
sage: designs.WittDesign(24) # optional - gap_packages Incidence structure with 24 points and 759 blocks
Or a Steiner Triple System on 19 points::
sage: designs.steiner_triple_system(19) (19,3,1)-Balanced Incomplete Block Design
**La Jolla Covering Repository**
The La Jolla Covering Repository (LJCR, see [1]_) is an online database of covering designs. As it is frequently updated, it is not included in Sage, but one can query it through :meth:`designs.best_known_covering_design_from_LJCR <sage.combinat.designs.covering_design.best_known_covering_design_www>`::
sage: C = designs.best_known_covering_design_from_LJCR(7, 3, 2) # optional - internet sage: C # optional - internet (7,3,2)-covering design of size 7 Lower bound: 7 Method: lex covering Submitted on: 1996-12-01 00:00:00 sage: C.incidence_structure() # optional - internet Incidence structure with 7 points and 7 blocks
**Design constructors**
This module gathers the following designs :
.. csv-table:: :class: contentstable :widths: 100 :delim: |
:meth:`~sage.combinat.designs.block_design.ProjectiveGeometryDesign` :meth:`~sage.combinat.designs.block_design.DesarguesianProjectivePlaneDesign` :meth:`~sage.combinat.designs.block_design.HughesPlane` :meth:`~sage.combinat.designs.database.HigmanSimsDesign` :meth:`~sage.combinat.designs.bibd.balanced_incomplete_block_design` :meth:`~sage.combinat.designs.resolvable_bibd.resolvable_balanced_incomplete_block_design` :meth:`~sage.combinat.designs.resolvable_bibd.kirkman_triple_system` :meth:`~sage.combinat.designs.block_design.AffineGeometryDesign` :meth:`~sage.combinat.designs.block_design.CremonaRichmondConfiguration` :meth:`~sage.combinat.designs.block_design.WittDesign` :meth:`~sage.combinat.designs.block_design.HadamardDesign` :meth:`~sage.combinat.designs.block_design.Hadamard3Design` :meth:`~sage.combinat.designs.latin_squares.mutually_orthogonal_latin_squares` :meth:`~sage.combinat.designs.orthogonal_arrays.transversal_design` :meth:`~sage.combinat.designs.orthogonal_arrays.orthogonal_array` :meth:`~sage.combinat.designs.orthogonal_arrays.incomplete_orthogonal_array` :meth:`~sage.combinat.designs.difference_family.difference_family` :meth:`~sage.combinat.designs.difference_matrices.difference_matrix` :meth:`~sage.combinat.designs.bibd.steiner_triple_system` :meth:`~sage.combinat.designs.steiner_quadruple_systems.steiner_quadruple_system` :meth:`~sage.combinat.designs.block_design.projective_plane`
And the :meth:`designs.best_known_covering_design_from_LJCR <sage.combinat.designs.covering_design.best_known_covering_design_www>` function which queries the LJCR.
.. TODO::
Implement DerivedDesign and ComplementaryDesign.
REFERENCES:
.. [1] La Jolla Covering Repository, http://www.ccrwest.org/cover.html """
from sage.combinat.designs.block_design import (BlockDesign, ProjectiveGeometryDesign, DesarguesianProjectivePlaneDesign, projective_plane, AffineGeometryDesign, WittDesign, HadamardDesign, Hadamard3Design, HughesPlane, CremonaRichmondConfiguration)
from .database import HigmanSimsDesign
from sage.combinat.designs.steiner_quadruple_systems import steiner_quadruple_system
from sage.combinat.designs.covering_design import best_known_covering_design_www as best_known_covering_design_from_LJCR
from sage.combinat.designs.latin_squares import mutually_orthogonal_latin_squares
from sage.combinat.designs.orthogonal_arrays import transversal_design, incomplete_orthogonal_array
from sage.combinat.designs.difference_family import difference_family from .difference_matrices import difference_matrix
from sage.combinat.designs.bibd import balanced_incomplete_block_design, steiner_triple_system from sage.combinat.designs.resolvable_bibd import resolvable_balanced_incomplete_block_design, kirkman_triple_system from sage.combinat.designs.group_divisible_designs import group_divisible_design
from .orthogonal_arrays import OAMainFunctions as orthogonal_arrays |