# 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)
Incidence structure with 19 points and 57 blocks


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 :

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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