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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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32,400,859 matroids, showing 7,001–7,050

label ▼	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
4.9.183213	4	9	99	16	✗	all but 2	1	rational
4.9.183212	4	9	100	8	✗	all	6	rational
4.9.183211	4	9	100	8	✗	all	5	rational
4.9.183210	4	9	100	4	✗	all	4	rational
4.9.183209	4	9	101	4	✗	∅	-1	rational
4.9.183208	4	9	101	8	✗	all	2	rational
4.9.183207	4	9	101	16	✗	all	1	rational
4.9.183206	4	9	102	16	✗	all	1	rational
4.9.183205	4	9	101	144	✗	all but 3	0	rational
4.9.183204	4	9	98	96	✗	all	6	rational
4.9.183203	4	9	100	12	✗	all	3	rational
4.9.183202	4	9	101	8	✗	all	1	rational
4.9.183201	4	9	102	24	✗	all	3	rational
4.9.183200	4	9	102	288	✗	all	4	rational
4.9.183199	4	9	103	288	✗	∅	-1	rational
4.9.183198	4	9	90	4	✓	all	3	empty
4.9.183197	4	9	96	6	✓	all	3	empty
4.9.183196	4	9	97	6	✓	all	2	empty
4.9.183195	4	9	88	192	✓	all	0	empty
4.9.183194	4	9	94	16	✓	all	1	empty
4.9.183193	4	9	97	48	✓	all	2	empty
4.9.183192	4	9	89	24	✓	all but 2,3,7	0	empty
4.9.183191	4	9	95	2	✓	all	2	empty
4.9.183190	4	9	98	6	✓	all	3	empty
4.9.183189	4	9	90	8	✓	all but 2	0	empty
4.9.183188	4	9	96	2	✓	all	0	empty
4.9.183187	4	9	96	4	✓	all	1	empty
4.9.183186	4	9	99	4	✓	all	4	empty
4.9.183185	4	9	91	6	✓	all	2	empty
4.9.183184	4	9	97	2	✓	∅	-1	empty
4.9.183183	4	9	100	6	✓	all	2	empty
4.9.183182	4	9	92	24	✓	∅	-1	empty
4.9.183181	4	9	98	8	✓	all	1	empty
4.9.183180	4	9	101	24	✓	all	4	empty
4.9.183179	4	9	90	4	✓	all	4	rational
4.9.183178	4	9	91	2	✓	all	3	rational
4.9.183177	4	9	97	2	✓	all	1	rational
4.9.183176	4	9	92	2	✓	all	5	rational
4.9.183175	4	9	97	2	✓	all	2	rational
4.9.183174	4	9	93	2	✓	all	1	rational
4.9.183173	4	9	97	2	✓	all	2	rational
4.9.183172	4	9	98	2	✓	all	1	rational
4.9.183171	4	9	95	4	✓	all	3	empty
4.9.183170	4	9	96	4	✓	all	1	rational
4.9.183169	4	9	96	2	✓	all but 2	1	empty
4.9.183168	4	9	98	4	✓	all	3	empty
4.9.183167	4	9	99	4	✓	all but 7	0	empty
4.9.183166	4	9	96	1	✓	all	2	empty
4.9.183165	4	9	97	1	✓	all but 2	1	empty
4.9.183164	4	9	97	2	✓	all	3	empty