Catalog of designsΒΆ

This module gathers all designs that can be reached from a Sage sessions through the designs objects. In order to create the Witt design on 24 points it is sufficient to type:

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

Online database – Jolla Covering Repository (LJCR) :

There exists an online database of the best known covering designs, the La Jolla Covering Repository (LJCR), available at [1]. As it is over 60MB and changes frequently that database is not included in Sage, but one can obtain individual coverings and block designs from the LJCR using the method 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

Currently, this module gathers the following designs :

ProjectiveGeometryDesign()
ProjectivePlaneDesign()
AffineGeometryDesign()
WittDesign()
HadamardDesign()
steiner_triple_system()
steiner_quadruple_system()

And the designs.best_known_covering_design_from_LJCR function which queries the LJCR.

Todo

Implement DerivedDesign, ComplementaryDesign, and Hadamard3Design

REFERENCES:

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

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