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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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3,621,120 matroids, showing 1,151–1,200

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
3.10.4731	3	10	108	4	✓	all	4	rational
3.10.4752	3	10	107	2	✓	all	4	rational
3.10.4772	3	10	105	1	✓	all	4	rational
3.10.4773	3	10	103	4	✓	all	4	rational
3.10.4774	3	10	104	2	✓	all	4	rational
3.10.4775	3	10	107	2	✓	all	4	rational
3.10.4778	3	10	106	2	✓	all	4	rational
3.10.4786	3	10	105	1	✓	all	4	empty
3.10.4852	3	10	105	1	✓	all	4	empty
3.10.4858	3	10	104	2	✓	all	4	empty
3.10.4859	3	10	105	4	✓	all	4	empty
3.10.4872	3	10	104	2	✓	all	4	empty
3.10.4931	3	10	101	2	✓	all	4	empty
3.10.4940	3	10	102	2	✓	all	4	empty
3.10.4943	3	10	104	24	✓	all	4	rational
3.10.4949	3	10	101	6	✓	all	4	empty
3.10.4952	3	10	108	1152	✗	all	4	rational
3.10.4960	3	10	105	8	✗	all	4	rational
3.10.4961	3	10	105	4	✗	all	4	rational
3.10.4974	3	10	102	48	✗	all	4	empty
3.10.4980	3	10	109	144	✗	all	4	rational
3.10.4990	3	10	108	8	✗	all	4	rational
3.10.4999	3	10	104	4	✗	all	4	rational
3.10.5004	3	10	106	8	✗	all	4	rational
3.10.5009	3	10	105	4	✗	all	4	rational
3.10.5027	3	10	106	8	✗	all	4	rational
3.10.5032	3	10	104	12	✗	all	4	rational
3.10.5033	3	10	104	16	✗	all	4	rational
3.10.5037	3	10	108	24	✗	all	4	rational
3.10.5039	3	10	107	4	✗	all	4	rational
3.10.5042	3	10	107	8	✗	all	4	rational
3.10.5049	3	10	105	2	✗	all	4	rational
3.10.5054	3	10	107	8	✗	all	4	rational
3.10.5055	3	10	106	8	✗	all	4	rational
3.10.5064	3	10	105	2	✗	all	4	rational
3.10.5070	3	10	104	2	✗	all	4	rational
3.10.5072	3	10	104	2	✗	all	4	rational
3.10.5078	3	10	102	8	✗	all	4	rational
3.10.5081	3	10	106	4	✗	all	4	rational
3.10.5093	3	10	105	2	✗	all	4	rational
3.10.5097	3	10	104	2	✗	all	4	rational
3.10.5103	3	10	104	4	✗	all	4	rational
3.10.5114	3	10	104	2	✗	all	4	rational
3.10.5115	3	10	105	4	✗	all	4	rational
3.10.5116	3	10	104	2	✗	all	4	rational
3.10.5126	3	10	103	2	✗	all	4	rational
3.10.5130	3	10	103	4	✗	all	4	rational
3.10.5138	3	10	104	16	✗	all	4	rational
3.10.5142	3	10	103	8	✗	all	4	rational
3.10.5146	3	10	105	8	✗	all	4	rational