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4 matroids

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.8.313849168✓{2}-1empty
3.8.136384548✓{2}-1rational
3.8.143384372✗{2}-1rational
3.8.179383448✗{2}-1rational