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325 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 3.8.0 | 3 | 8 | 56 | 40320 | ✓ | all | 8 | rational |
| 3.8.1 | 3 | 8 | 55 | 720 | ✓ | all | 7 | rational |
| 3.8.2 | 3 | 8 | 54 | 144 | ✓ | all | 6 | rational |
| 3.8.3 | 3 | 8 | 54 | 48 | ✓ | all | 6 | rational |
| 3.8.4 | 3 | 8 | 53 | 48 | ✓ | all | 5 | rational |
| 3.8.5 | 3 | 8 | 53 | 8 | ✓ | all | 5 | rational |
| 3.8.6 | 3 | 8 | 52 | 8 | ✓ | all | 4 | rational |
| 3.8.7 | 3 | 8 | 53 | 48 | ✓ | all | 5 | rational |
| 3.8.8 | 3 | 8 | 53 | 12 | ✓ | all | 5 | rational |
| 3.8.9 | 3 | 8 | 52 | 4 | ✓ | all | 4 | rational |
| 3.8.10 | 3 | 8 | 52 | 4 | ✓ | all | 4 | rational |
| 3.8.11 | 3 | 8 | 52 | 4 | ✓ | all | 4 | rational |
| 3.8.12 | 3 | 8 | 51 | 4 | ✓ | all | 3 | rational |
| 3.8.13 | 3 | 8 | 51 | 2 | ✓ | all | 3 | rational |
| 3.8.14 | 3 | 8 | 50 | 12 | ✓ | all | 2 | rational |
| 3.8.15 | 3 | 8 | 52 | 6 | ✓ | all | 4 | rational |
| 3.8.16 | 3 | 8 | 51 | 2 | ✓ | all | 3 | rational |
| 3.8.17 | 3 | 8 | 51 | 2 | ✓ | all | 3 | rational |
| 3.8.18 | 3 | 8 | 50 | 2 | ✓ | all | 2 | rational |
| 3.8.19 | 3 | 8 | 51 | 12 | ✓ | all | 3 | rational |
| 3.8.20 | 3 | 8 | 50 | 2 | ✓ | all | 2 | rational |
| 3.8.21 | 3 | 8 | 49 | 6 | ✓ | all | 1 | rational |
| 3.8.22 | 3 | 8 | 48 | 48 | ✓ | all | 0 | point over Q(a)/(a^2 - a + 1) |
| 3.8.23 | 3 | 8 | 52 | 48 | ✓ | all | 4 | rational |
| 3.8.24 | 3 | 8 | 51 | 8 | ✓ | all | 3 | rational |
| 3.8.25 | 3 | 8 | 51 | 8 | ✓ | all | 3 | rational |
| 3.8.26 | 3 | 8 | 50 | 2 | ✓ | all | 2 | rational |
| 3.8.27 | 3 | 8 | 50 | 8 | ✓ | all | 2 | rational |
| 3.8.28 | 3 | 8 | 49 | 4 | ✓ | all | 1 | rational |
| 3.8.29 | 3 | 8 | 50 | 24 | ✓ | all but 2 | 2 | rational |
| 3.8.30 | 3 | 8 | 49 | 8 | ✓ | all but 2 | 1 | rational |
| 3.8.31 | 3 | 8 | 49 | 168 | ✓ | {2} | -1 | empty |
| 3.8.32 | 3 | 8 | 50 | 1440 | ✗ | all | 1 | rational |
| 3.8.33 | 3 | 8 | 49 | 72 | ✗ | all | 1 | rational |
| 3.8.34 | 3 | 8 | 48 | 144 | ✗ | all | 0 | rational |
| 3.8.35 | 3 | 8 | 48 | 16 | ✗ | all | 2 | rational |
| 3.8.36 | 3 | 8 | 47 | 12 | ✗ | all | 2 | rational |
| 3.8.37 | 3 | 8 | 46 | 48 | ✗ | all | 2 | rational |
| 3.8.38 | 3 | 8 | 35 | 5040 | ✗ | all | 1 | rational |
| 3.8.39 | 3 | 8 | 52 | 576 | ✓ | all | 6 | rational |
| 3.8.40 | 3 | 8 | 51 | 144 | ✓ | all | 5 | rational |
| 3.8.41 | 3 | 8 | 48 | 1152 | ✓ | all | 4 | rational |
| 3.8.42 | 3 | 8 | 51 | 24 | ✓ | all | 4 | rational |
| 3.8.43 | 3 | 8 | 50 | 12 | ✓ | all | 3 | rational |
| 3.8.44 | 3 | 8 | 50 | 16 | ✓ | all | 2 | rational |
| 3.8.45 | 3 | 8 | 50 | 48 | ✓ | all | 6 | rational |
| 3.8.46 | 3 | 8 | 50 | 4 | ✓ | all | 6 | rational |
| 3.8.47 | 3 | 8 | 49 | 4 | ✓ | all | 5 | rational |
| 3.8.48 | 3 | 8 | 49 | 2 | ✓ | all | 4 | rational |
| 3.8.49 | 3 | 8 | 48 | 8 | ✓ | all | 5 | rational |