## Catalogue of Nice Error Bases

### Andreas Klappenecker and Martin Rötteler.

Nice unitary error bases have been introduced by Knill as a generalization of the Pauli basis.
Our aim is to give information about all nice error bases of small degree.

### 2-Dimensional Bases

Abelian Group G(4,2)

### 3-Dimensional Bases

Abelian Group G(9,2)

### 4-Dimensional Bases

Abelian Group G(16,2)
Abelian Group G(16,14)
Nonabelian Group G(16,3)
Nonabelian Group G(16,11)

### 5-Dimensional Bases

Abelian Group G(25,2)

### 6-Dimensional Bases

Abelian Group G(36,14)
Nonabelian Group G(36,11)
Nonabelian Group G(36,13)

### 7-Dimensional Bases

Abelian Group G(49,2)

### 8-Dimensional Bases (only nonabelian index groups)

Nonabelian Group G(64,3)
Nonabelian Group G(64,8)
Nonabelian Group G(64,10)
Nonabelian Group G(64,34)
Nonabelian Group G(64,35)
Nonabelian Group G(64,58)
Nonabelian Group G(64,60)
Nonabelian Group G(64,62)
Nonabelian Group G(64,67)
Nonabelian Group G(64,68)
Nonabelian Group G(64,69)
Nonabelian Group G(64,71)
Nonabelian Group G(64,72)
Nonabelian Group G(64,73)
Nonabelian Group G(64,74)
Nonabelian Group G(64,75)
Nonabelian Group G(64,77)
Nonabelian Group G(64,78)
Nonabelian Group G(64,82)
Nonabelian Group G(64,90)
Nonabelian Group G(64,91)
Nonabelian Group G(64,123)
Nonabelian Group G(64,128)
Nonabelian Group G(64,138)
Nonabelian Group G(64,162)
Nonabelian Group G(64,167)
Nonabelian Group G(64,174)
Nonabelian Group G(64,179)
Nonabelian Group G(64,193)
Nonabelian Group G(64,195)
Nonabelian Group G(64,202)
Nonabelian Group G(64,203)
Nonabelian Group G(64,207)
Nonabelian Group G(64,211)
Nonabelian Group G(64,216)
Nonabelian Group G(64,226)
Nonabelian Group G(64,236)
Nonabelian Group G(64,242)
Nonabelian Group G(64,261)

### 9-Dimensional Bases (only nonabelian index groups)

Nonabelian Group G(81,4)
Nonabelian Group G(81,9)
Nonabelian Group G(81,12)
Nonabelian Group G(81,12)

### 10-Dimensional Bases (only nonabelian index groups)

Nonabelian Group G(100,15)