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Size rank n

Invariants Bases Automorphisms Dimension of realization space Girth Expected dimension over ℤ

Realizability realizable in char 0 realizable in characteristic char set class birational type

Properties Simple Connected Paving Uniform Regular Binary Ternary Quaternary Graphic Transversal Series parallel Self dual Orientable Supersolvable Three lines Free realization space Realization space: smooth over ℤ Realization space: is regular scheme

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2,017,782 matroids, showing 9,551–9,600

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	birational type ⇅
3.11.298251	3	11	40	2880	✗	all	rational
3.11.298259	3	11	36	1440	✗	all but 2,3,5	rational
3.11.298267	3	11	33	1440	✗	all but 2	rational
3.11.298277	3	11	28	192	✗	all	rational
3.11.298280	3	11	27	576	✗	all but 2,5	rational
3.11.298303	3	11	15	1440	✗	all	rational
3.11.298310	3	11	30	20160	✗	all	rational
3.11.298313	3	11	33	1440	✗	all	rational
3.11.298323	3	11	25	960	✗	all but 2,7	rational
3.11.298326	3	11	24	576	✗	all	rational
3.11.298378	3	11	35	10080	✗	all	rational
3.11.298379	3	11	34	960	✗	all	rational
3.11.298398	3	11	27	1296	✗	all	rational
3.11.298409	3	11	29	2880	✗	all	rational
3.11.298441	3	11	18	864	✗	all	rational
3.11.298448	3	11	10	14400	✗	all	rational
3.11.298452	3	11	21	4320	✗	all	rational
3.11.298469	3	11	15	10080	✗	all but 2,3,5,7	rational
3.12.19	3	12	215	16	✓	all but 2,3,5	?
3.12.46	3	12	215	96	✓	all but 2,3,7	?
3.12.53	3	12	215	8	✓	all but 2,5	?
3.12.66	3	12	213	4	✓	all but 2	?
3.12.76	3	12	215	2304	✓	all but 2,3,7	?
3.12.82	3	12	215	432	✓	all but 2,3,7	?
3.12.119	3	12	213	4	✓	all but 2,7	?
3.12.126	3	12	213	4	✓	all but 2,3,5	?
3.12.138	3	12	213	8	✓	all but 2,3,5,11	?
3.12.152	3	12	214	2	✓	all but 2,3,7	?
3.12.153	3	12	213	2	✓	all but 2,3,7	?
3.12.161	3	12	214	8	✓	all but 2,3,5	?
3.12.169	3	12	213	2	✓	all but 2,7	?
3.12.188	3	12	213	2	✓	all but 2,3,5	?
3.12.202	3	12	214	2	✓	all but 2,3,5	?
3.12.258	3	12	213	4	✓	all but 2,3,5	?
3.12.281	3	12	213	2	✓	all but 2,5	?
3.12.293	3	12	213	1	✓	all but 2,3	?
3.12.318	3	12	212	1	✓	all but 2	?
3.12.335	3	12	212	1	✓	all but 2,3	?
3.12.348	3	12	213	2	✓	all but 2,17	?
3.12.369	3	12	214	4	✓	all but 2	?
3.12.370	3	12	213	1	✓	all but 2,3,7	?
3.12.372	3	12	213	2	✓	all but 2,5	?
3.12.412	3	12	212	1	✓	all but 2	?
3.12.420	3	12	212	1	✓	all but 2,3,7	?
3.12.436	3	12	212	3	✓	all but 2,3,7	?
3.12.451	3	12	211	2	✓	all but 2,3	?
3.12.456	3	12	211	2	✓	all but 2,5	?
3.12.468	3	12	212	1	✓	all but 2	?
3.12.477	3	12	213	4	✓	all but 2,3,7	?
3.12.495	3	12	212	1	✓	all but 2,3,5	?