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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