Graphical Designs on the 7-dimensional Cube Graph

Graph Info
Vertices	128
Edges	448
Regularity	7
Eigenspaces	8

Spectrum from low to high frequency:

`0,-2,-0.2857^{7}, -1.71429^7, -0.5714^{20}, -1.42859^{20}, -0.8571^{35}, -1.14289^{35}`

4 Design on the 7-Cube Graph

Design Info
`k`-graphical design	`k=4`
Efficacy	`8/16`
Optimal	no
Maximal	no
Extremal	no
1-Neighborhood is the graph	no

7-Cube Graph

Design Info
`k`-graphical design	`k=7`
Efficacy	`16/93`
Optimal	yes
Maximal	yes
Extremal	yes
1-Neighborhood is the graph	yes

The (7,4) Hamming Code is a 7-graphical design with all of these properties.

Get the code or see Wikipedia for more about cube graphs.