Links on this page

BIBDs, PBDs etc | NBIBDs | OBIBDs| ONBIBDs|

Background Information

Home page
List of applets
System requirements and limitations
References
Site Map
What's new?

BIBDs, PBDs etc

Home page for BIBDs

Solutions

BIBDs with v = 7
BIBDs with v = 8
BIBDs with v = 9
BIBDs with v = 10
BIBDs with v = 11
BIBDs with v = 12
BIBDs with v = 13
BIBDs with v = 14
BIBDs with v = 15
BIBDs with v = 16
BIBDs with v = 17
BIBDs with v = 18
BIBDs with v = 19
BIBDs with v = 20
BIBDs with v = 21
BIBDs with v = 22
BIBDs with v = 23
BIBDs with v = 24
BIBDs with v = 25
BIBDs with v = 26

Constructions

Netto BIBDs from d.h. groups

Geometric constructions: subgeometries of PG(k,pνρ)

Overview
k=2,ρ>2
k=2,ρ>2 and composite
applet for above
k>2,ρ=2
applet for above
Plane of type B1 from PG(3,q2ν)
Hyperplane of type D1 from PG(4,q2ν)
k=3,ρ=3
k=2,ρ=3, Type B1
k=2,ρ=3, Type B2
k=3,ρ=4, q=2
k=2,ρ=4, q=2, Type B1
k=2,ρ=4, q=2, Another Type B1
k=2,ρ=4, q=2, Type B2
k=2,ρ=4, q=2, Type B3
k=3,ρ=4, q=3
k=2,ρ=4, q=3, Type B1
k=2,ρ=4, q=3, Another Type B1
k=2,ρ=4, q=3, Type B2
k=2,ρ=4, q=3, Type B3
k=4,ρ=3, q=2 Introduction
k=3,ρ=3, q=2, Type D1
k=2,ρ=3, q=2, Type B1, from D1
k=2,ρ=3, q=2, Type B2, from D1
k=2,ρ=3, q=2, Type B3 from D1
k=3,ρ=3, q=2, Type D2

Nested BIBDs

Home page for NBIBDs

Definition

NBIBD Definition

Constructions

Construction of NBIBDs from d.h. groups
Applet for NBIBDs from d.h. groups
NBIBDs from d.h. groups with block sizes 9 and 3
NBIBDs from d.h. groups with bloc sizes 15 and 3
NBIBDs from d.h. groups with block sizes 15 and 5
NBIBDs from d.h. groups with block sizes 21 and 3
NBIBDs from d.h. groups with block sizes 21 and 7
Links to NBIBDs from additive subgroups of d.h. groups
Actual NBIBDs from additive subgroups of d.h. groups

Solutions

NBIBDs with v = 8
NBIBDs with v = 12
NBIBDs with v = 16
NBIBDs with v = 18
NBIBDs with v = 20
NBIBDs with v = 21
NBIBDs with v = 22
Table of small NBIBDs

Existence

Overview
Theorems
NBIBDs in blocks of 6 and 2
NBIBDs in blocks of 6 and 3
Incomplete NBIBDs with main block size 6

Other Nested Designs

Other nested designs
Construction of Nested 3-design
Nested 3-designs example
Table of nested 3-designs

Orthogonal BIBDs

Home page for OBIBDs

Definitions

OBIBD Definition
Definition of Difference Squares

Constructions

Home page for constructions of OBIBDs
OBIBDs from d.h. groups, with k = 3
OBIBDs from d.h. groups, with k > 3
Applet showing how to construct OBIBDs with block size 3 and λ 2.
Applet to find multipliers m for OBIBDs from d.h. groups
Applet to get blocks of OBIBDs from d.h. groups, given m etc
Tables for OBIBD construction from d.h. groups, with k = 3
Tables for OBIBD construction from d.h. groups, with k = 5
Tables for OBIBD construction from d.h. groups, with k = 7
Tables for OBIBD construction from d.h. groups, with k > 9
OBIBD Construction with λ = 1, and k = 5,7
Tables for OBIBD construction with λ = 1 and k = 5
Tables for OBIBD construction with λ = 1 and k = 7
OBIBDs from Projective Geometries
Example of previous
OBIBDs from Projective Geometries, using Singer-type collineations
Example of previous
OBIBDs from rings
OBIBDs from rings, continued
Examples of OBIBDs from rings
Tables for OBIBD construction from rings

Solutions

OBIBDs with v = 8
OBIBDs with v = 12
OBIBDs with v = 16
OBIBDs with v = 18
OBIBDs with v = 20

Properties

Overview of OBIBD properties
Example of OBIBD properties (v=19)
Correlations (for v=19)
Example of OBIBD properties (v=15)
Relationship between OBIBDs and other designs
OBIBD relationships as difference patterns

Orthogonal Nested BIBDs

Home page for ONBIBDs

Definition

Definition of Orthogonal Nested BIBDs

Constructions
Solutions

Nested Pergolas with v = 8
Nested Pergolas with v = 16

Last Updated on 20/10/2004
By D.H.Rees