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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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16,388 matroids, showing 1–50

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
3.8.0	3	8	56	40320	✓	all	8	rational
3.9.2	3	9	82	432	✓	all	8	rational
3.9.4	3	9	82	192	✓	all	8	rational
3.9.182	3	9	79	72	✓	all	8	rational
3.9.196	3	9	77	4	✓	all	8	rational
3.9.197	3	9	77	4	✓	all	8	rational
3.10.6	3	10	116	128	✓	all	8	rational
3.10.8	3	10	116	48	✓	all	8	rational
3.10.9	3	10	116	8	✓	all	8	rational
3.10.11	3	10	116	48	✓	all	8	rational
3.10.12	3	10	116	16	✓	all	8	rational
3.10.18	3	10	116	288	✓	all	8	rational
3.10.19	3	10	116	16	✓	all	8	rational
3.10.21	3	10	116	384	✓	all	8	rational
3.10.23	3	10	116	36	✓	all	8	rational
3.10.24	3	10	116	8	✓	all	8	rational
3.10.33	3	10	116	8	✓	all	8	rational
3.10.59	3	10	116	24	✓	all	8	rational
3.10.161	3	10	115	4	✓	all	8	rational
3.10.1034	3	10	112	4	✓	all	8	rational
3.10.1771	3	10	109	16	✓	all	8	rational
3.10.1772	3	10	109	144	✓	all	8	empty
3.10.1804	3	10	111	2	✓	all	8	rational
3.10.1805	3	10	111	2	✓	all	8	rational
3.10.1808	3	10	111	1	✓	all	8	rational
3.10.1810	3	10	111	2	✓	all	8	rational
3.10.1812	3	10	111	2	✓	all	8	rational
3.10.1821	3	10	111	1	✓	all	8	rational
3.10.1838	3	10	112	2	✓	all	8	rational
3.10.1861	3	10	111	2	✓	all	8	rational
3.10.3975	3	10	109	4	✓	all	8	rational
3.10.4814	3	10	102	2	✓	all	8	empty
3.10.6547	3	10	79	8	✗	all	8	rational
3.10.6703	3	10	103	12	✓	all	8	rational
3.10.6731	3	10	104	2	✓	all	8	rational
3.10.6738	3	10	105	4	✓	all	8	rational
3.10.7942	3	10	77	8	✗	all	8	rational
3.10.8293	3	10	82	24	✗	all	8	rational
3.10.8460	3	10	65	2	✗	all	8	rational
3.10.8522	3	10	50	4	✗	all	8	rational
3.10.8621	3	10	91	4	✗	all	8	rational
3.10.8956	3	10	68	288	✗	all	8	rational
3.10.9000	3	10	73	48	✗	all	8	rational
3.10.9344	3	10	42	32	✗	all	8	rational
3.10.9973	3	10	24	1152	✗	all	8	rational
3.10.10018	3	10	13	1440	✗	all	8	rational
3.11.18	3	11	159	4	✓	all	8	rational
3.11.19	3	11	159	4	✓	all	8	rational
3.11.21	3	11	159	8	✓	all	8	rational
3.11.22	3	11	159	8	✓	all	8	rational