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OBIBDs (Orthogonal Balanced Incomplete Block Designs)
Overview
Definition
Constructions ▼
Existence ▼
Properties ▼
Searches ▼
Overview
From doubly homogeneous groups
▶
Designs with λ=1 and k>3
▶
Geometric construction
▶
Construction from rings
▶
Overview
Applet for k=3
Overview
Related designs
▶
Geometric Examples
▶
Difference Squares
Overview
v=8
v=12
v=16
v=18
v=20
Construction: k=3
Construction: k>3
Table of multipliers: k=3
Table of multipliers: k=5
Table of multipliers: k=7
Table of multipliers: k>7
Applet to get multiplier
Applet to get blocks
Construction
Example
Construction contd
Example contd
Construction
Table of multipliers: k=5
Table of multipliers: k=7
Construction
Examples
Table of multipliers
Discussion
Difference patterns
OBIBD from a PG
OBIBD from a Netto BIBD
Correlations
m
values for use in OBIBD construction for designs with
r
= (
v
-1)/2 and
k
= 9 or more.
k
t
v
x
m
9
10
379
2
21
9
14
523
2
29
9
20
739
3
41
9
24
883
2
28,70
9
35
1279
3
56,86
9
42
1531
2
35,135
9
48
1747
2
5,189
11
61
2707
2
117,129
11
67
2971
10
135
11
87
3851
2
22,328
13
88
4603
2
117,237