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6 matroids

label ▲rank ⇅n ⇅#bases ⇅#automorphisms ⇅simple ⇅char set ⇅rs dim ⇅birational type ⇅
3.11.031116539916800✓all14rational
3.12.1631221520✓all14?
3.12.673122122✓all14?
3.12.162029253122011✓all14?
3.12.162281573122031✓all14?
3.12.162281653122021✓all14?