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209 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 |
| 3.8.8 | 3 | 8 | 53 | 12 | ✓ | all | 5 | rational |
| 3.8.32 | 3 | 8 | 50 | 1440 | ✗ | all | 1 | rational |
| 3.8.33 | 3 | 8 | 49 | 72 | ✗ | all | 1 | 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 |
| 3.8.46 | 3 | 8 | 50 | 4 | ✓ | all | 6 | rational |
| 3.8.62 | 3 | 8 | 48 | 72 | ✓ | all | 3 | rational |
| 3.8.63 | 3 | 8 | 47 | 8 | ✓ | all | 2 | rational |
| 3.8.66 | 3 | 8 | 46 | 96 | ✗ | all | 1 | rational |
| 3.8.68 | 3 | 8 | 48 | 96 | ✗ | all | 1 | rational |
| 3.8.69 | 3 | 8 | 47 | 24 | ✗ | all | 0 | rational |
| 3.8.70 | 3 | 8 | 44 | 96 | ✗ | all | 3 | rational |
| 3.8.71 | 3 | 8 | 47 | 8 | ✗ | all | 3 | rational |
| 3.8.79 | 3 | 8 | 44 | 12 | ✗ | all | 1 | rational |
| 3.8.81 | 3 | 8 | 46 | 32 | ✗ | all | 2 | rational |
| 3.8.82 | 3 | 8 | 45 | 8 | ✗ | all | 0 | rational |
| 3.8.84 | 3 | 8 | 45 | 4 | ✗ | all | 3 | rational |
| 3.8.91 | 3 | 8 | 42 | 8 | ✗ | all | 4 | rational |
| 3.8.99 | 3 | 8 | 44 | 192 | ✗ | all | 1 | rational |
| 3.8.102 | 3 | 8 | 42 | 16 | ✗ | all | 0 | rational |
| 3.8.104 | 3 | 8 | 40 | 32 | ✗ | all | 2 | rational |
| 3.8.106 | 3 | 8 | 40 | 8 | ✗ | all | 0 | rational |
| 3.8.110 | 3 | 8 | 38 | 96 | ✗ | all | 3 | rational |
| 3.8.113 | 3 | 8 | 34 | 144 | ✗ | all | 0 | rational |
| 3.8.114 | 3 | 8 | 33 | 72 | ✗ | all | 1 | rational |
| 3.8.115 | 3 | 8 | 33 | 16 | ✗ | all but 2 | 0 | rational |
| 3.8.116 | 3 | 8 | 32 | 8 | ✗ | all | 2 | rational |
| 3.8.118 | 3 | 8 | 32 | 6 | ✗ | all | 4 | rational |
| 3.8.126 | 3 | 8 | 40 | 720 | ✗ | all | 0 | rational |
| 3.8.127 | 3 | 8 | 39 | 72 | ✗ | all | 3 | rational |
| 3.8.129 | 3 | 8 | 36 | 144 | ✗ | all | 2 | rational |
| 3.8.130 | 3 | 8 | 30 | 240 | ✗ | all | 1 | rational |
| 3.8.131 | 3 | 8 | 29 | 24 | ✗ | all | 3 | rational |
| 3.8.133 | 3 | 8 | 20 | 1440 | ✗ | all | 1 | rational |
| 3.8.134 | 3 | 8 | 46 | 720 | ✓ | all but 2 | 1 | rational |
| 3.8.135 | 3 | 8 | 45 | 720 | ✓ | all but 2 | 0 | rational |
| 3.8.136 | 3 | 8 | 45 | 48 | ✓ | {2} | -1 | rational |
| 3.8.137 | 3 | 8 | 44 | 12 | ✓ | all | 4 | rational |
| 3.8.139 | 3 | 8 | 42 | 144 | ✓ | all | 2 | rational |