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 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()

HughesPlane()

HigmanSimsDesign()

balanced_incomplete_block_design()

resolvable_balanced_incomplete_block_design()

kirkman_triple_system()

AffineGeometryDesign()

CremonaRichmondConfiguration()

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()

biplane()

gen_quadrangles_with_spread()

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, https://math.ccrwest.org/cover.html