Cubic cages of small girth

The cages

n(3,g)

Range

Number

Reference

(3,3)-cages

4

4

1

K_4

(3,4)-cages

6

6

1

K_3,3

(3,5)-cages

10

10

1

Petersen

(3,6)-cages

14

14

1

Heawood

(3,7)-cages

22

24

1

McGee graph 

(3,8)-cages

30

30

1

Tutte's 8-cage

(3,9)-cages

46

58

18

Brinkmann & al.

(3,10)-cages

62

70

3

O'Keefe/Wong

(3,11)-cages

94

112

1+

McKay/Myrvold

(3,12)-cages

126

126

1

Gener. hexagon

(3,13)-cages

190

202-272

1+

McKay/Myrvold-Ho.

(3,14)-cages

254

258-384

1+

McKay - Exoo

(3,15)-cages

382

384-620

1+

Biggs

(3,16)-cages

510

512-960

1+

Exoo (12-02)

(3,17)-cages

766

768-2408

1+

Exoo (12-02)

(3,18)-cages

1022

1024-2688

1+

Bray (01-03)

(3,19)-cages

1534

1536-4324

1+

H(47)

(3,20)-cages

2046

2048-6072

1+

Parker/Rowley (01-03)

(3,21)-cages

3070

3072-16112

1+

Biggs/Whitehead

(3,22)-cages

4094

4096-16206

1+

Whitehead S(73)

(3,23)-cages

6142

6144-49482

1+

Bray/Parker/Ro.

(3,24)-cages

8190

8192-49608

1+

Bray/Parker/Ro.

(3,25)-cages

12286

12288-109010

1+

Bray/Parker/Ro.

(3,26)-cages

16382

16384-109200

1+

Bray/Pa./Rowley

(3,27)-cages

24574

24576-285852

1+

Bray/Pa./Rowley

(3,28)-cages

32766

32768-415104

1+

Bray/Pa./Rowley

(3,29)-cages

49150

49152-1143408

1+

Bray/Pa./Rowley

(3,30)-cages

65534

65536-1227666

1+

Hoare S(313)