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86 matroids, showing 1–50
| label ▲ | rank ⇅ | n ⇅ | #bases ⇅ | #automorphisms ⇅ | simple ⇅ | char set ⇅ | rs dim ⇅ | birational type ⇅ |
|---|---|---|---|---|---|---|---|---|
| 4.8.589 | 4 | 8 | 36 | 1152 | ✓ | all | 1 | rational |
| 4.8.672 | 4 | 8 | 40 | 8 | ✓ | all | 2 | rational |
| 4.8.673 | 4 | 8 | 32 | 48 | ✗ | all | 3 | rational |
| 4.8.709 | 4 | 8 | 39 | 12 | ✓ | all | 1 | rational |
| 4.8.711 | 4 | 8 | 37 | 16 | ✓ | all | 2 | rational |
| 4.8.712 | 4 | 8 | 36 | 48 | ✓ | all | 1 | rational |
| 4.8.715 | 4 | 8 | 30 | 96 | ✗ | all | 1 | rational |
| 4.8.717 | 4 | 8 | 30 | 24 | ✗ | all | 0 | rational |
| 4.8.718 | 4 | 8 | 24 | 192 | ✗ | all | 4 | rational |
| 4.8.733 | 4 | 8 | 34 | 4 | ✗ | all | 1 | rational |
| 4.8.735 | 4 | 8 | 33 | 16 | ✗ | all | 1 | rational |
| 4.8.736 | 4 | 8 | 32 | 16 | ✗ | all | 1 | rational |
| 4.8.741 | 4 | 8 | 31 | 8 | ✗ | all | 2 | rational |
| 4.8.742 | 4 | 8 | 28 | 96 | ✗ | all | 4 | rational |
| 4.8.753 | 4 | 8 | 26 | 8 | ✗ | all | 1 | rational |
| 4.8.755 | 4 | 8 | 25 | 32 | ✗ | all | 1 | rational |
| 4.8.756 | 4 | 8 | 24 | 32 | ✗ | all | 1 | rational |
| 4.8.759 | 4 | 8 | 20 | 32 | ✗ | all | 1 | rational |
| 4.8.760 | 4 | 8 | 16 | 384 | ✗ | all | 2 | rational |
| 4.8.772 | 4 | 8 | 21 | 8 | ✗ | all | 2 | rational |
| 4.8.773 | 4 | 8 | 20 | 48 | ✗ | all | 1 | rational |
| 4.8.781 | 4 | 8 | 24 | 48 | ✗ | all | 2 | rational |
| 4.8.789 | 4 | 8 | 16 | 16 | ✗ | all | 1 | rational |
| 4.8.795 | 4 | 8 | 30 | 720 | ✓ | all | 0 | rational |
| 4.8.799 | 4 | 8 | 27 | 72 | ✗ | all | 0 | rational |
| 4.8.803 | 4 | 8 | 24 | 48 | ✗ | all | 0 | rational |
| 4.8.806 | 4 | 8 | 18 | 144 | ✗ | all | 2 | rational |
| 4.8.810 | 4 | 8 | 21 | 72 | ✗ | all | 2 | rational |
| 4.8.814 | 4 | 8 | 18 | 72 | ✗ | all | 0 | rational |
| 4.8.818 | 4 | 8 | 15 | 24 | ✗ | all | 2 | rational |
| 4.8.821 | 4 | 8 | 12 | 48 | ✗ | all | 0 | rational |
| 4.8.824 | 4 | 8 | 9 | 144 | ✗ | all | 0 | rational |
| 4.8.845 | 4 | 8 | 28 | 168 | ✓ | all | 0 | empty |
| 4.8.854 | 4 | 8 | 28 | 6 | ✓ | all | 0 | rational |
| 4.8.855 | 4 | 8 | 27 | 72 | ✓ | all | 0 | rational |
| 4.8.861 | 4 | 8 | 24 | 12 | ✗ | all | 0 | rational |
| 4.8.864 | 4 | 8 | 24 | 8 | ✗ | all | 0 | rational |
| 4.8.868 | 4 | 8 | 21 | 8 | ✗ | all | 0 | rational |
| 4.8.874 | 4 | 8 | 16 | 24 | ✗ | all | 0 | rational |
| 4.8.877 | 4 | 8 | 18 | 144 | ✗ | all | 5 | rational |
| 4.8.882 | 4 | 8 | 24 | 48 | ✓ | all | 3 | rational |
| 4.8.883 | 4 | 8 | 20 | 240 | ✗ | all | 2 | rational |
| 4.8.885 | 4 | 8 | 22 | 8 | ✗ | all | 1 | rational |
| 4.8.886 | 4 | 8 | 21 | 24 | ✗ | all | 2 | rational |
| 4.8.887 | 4 | 8 | 18 | 24 | ✗ | all | 1 | rational |
| 4.8.889 | 4 | 8 | 20 | 16 | ✗ | {2} | -1 | rational |
| 4.8.890 | 4 | 8 | 19 | 8 | ✗ | all | 4 | rational |
| 4.8.891 | 4 | 8 | 16 | 16 | ✗ | all | 3 | rational |
| 4.8.893 | 4 | 8 | 15 | 12 | ✗ | all | 4 | rational |
| 4.8.894 | 4 | 8 | 12 | 48 | ✗ | all | 4 | rational |