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# Catalog of designs

This module gathers all designs that can be reached through `designs.<tab>`. Example with the 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 `designs.best_known_covering_design_from_LJCR`:

    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 :

`ProjectiveGeometryDesign()`
`DesarguesianProjectivePlaneDesign()`
`balanced_incomplete_block_design()`
`AffineGeometryDesign()`
`WittDesign()`
`HadamardDesign()`
`Hadamard3Design()`
`mutually_orthogonal_latin_squares()`
`transversal_design()`
`orthogonal_array()`
`incomplete_orthogonal_array()`
`difference_family()`
`difference_matrix()`
`steiner_triple_system()`
`steiner_quadruple_system()`
`projective_plane()`

And the `designs.best_known_covering_design_from_LJCR` function which queries the LJCR.

Todo

Implement DerivedDesign and ComplementaryDesign.

REFERENCES:

[1] | La Jolla Covering Repository, http://www.ccrwest.org/cover.html

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