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_package_design
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: