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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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2,575 matroids, showing 1–50

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
3.11.98244	3	11	144	48	✓	∅	-1	empty
3.11.211032	3	11	140	20	✓	∅	-1	point over Q(a)/(a^2 - a - 1)
3.11.211058	3	11	142	4	✓	all	1	empty
3.11.211062	3	11	141	4	✓	all	2	empty
3.11.211070	3	11	141	6	✓	all but 2	1	empty
3.11.220619	3	11	138	36	✓	∅	-1	point over Q(a)/(a^2 - a + 1)
3.11.221016	3	11	140	8	✓	∅	-1	empty
3.11.221029	3	11	139	12	✓	{5}	-1	empty
3.11.221034	3	11	140	6	✓	all but 2	1	empty
3.11.221039	3	11	139	2	✓	all but 2,5	0	empty
3.11.242883	3	11	137	4	✗	all	2	empty
3.11.242887	3	11	136	32	✗	all	2	rational
3.11.246271	3	11	134	24	✗	all	3	point over Q(a)/(a^2 - a + 1)
3.11.246970	3	11	136	8	✗	all	3	empty
3.11.246976	3	11	135	4	✗	all	2	empty
3.11.247077	3	11	134	4	✗	all	2	point over Q(a)/(a^2 - a - 1)
3.11.247087	3	11	135	2	✗	all	4	empty
3.11.248104	3	11	133	4	✗	all	3	empty
3.11.249332	3	11	132	48	✗	all	1	rational
3.11.249497	3	11	131	8	✗	all	3	empty
3.11.249539	3	11	129	8	✗	all	0	point over Q(a)/(a^2 - a - 1)
3.11.249562	3	11	127	48	✗	all	1	point over Q(a)/(a^2 - a + 1)
3.11.249623	3	11	130	16	✗	all	2	rational
3.11.249692	3	11	126	48	✗	all	3	rational
3.11.249718	3	11	120	3840	✗	∅	-1	rational
3.11.256440	3	11	140	120	✓	all	5	empty
3.11.261968	3	11	138	36	✓	all	1	point over Q(a)/(a^2 - a + 1)
3.11.262260	3	11	138	12	✓	all	4	empty
3.11.262780	3	11	136	24	✓	all	3	empty
3.11.262790	3	11	138	2	✓	all	1	empty
3.11.262808	3	11	137	2	✓	all	4	empty
3.11.262966	3	11	136	32	✓	all	3	empty
3.11.262970	3	11	135	12	✓	all	4	point over Q(a)/(a^2 - a + 1)
3.11.263615	3	11	128	96	✗	all but 2	2	rational
3.11.263732	3	11	132	8	✗	all	4	point over Q(a)/(a^2 - a - 1)
3.11.263734	3	11	131	6	✗	all	4	point over Q(a)/(a^2 - a + 1)
3.11.263797	3	11	131	4	✗	all	2	empty
3.11.268326	3	11	136	8	✗	all	7	empty
3.11.268340	3	11	135	24	✗	all	2	empty
3.11.268446	3	11	135	8	✗	all	4	rational
3.11.273174	3	11	134	12	✗	all but 2,5	0	empty
3.11.274705	3	11	133	8	✗	all	2	rational
3.11.275313	3	11	133	2	✗	all	5	point over Q(a)/(a^2 - a - 1)
3.11.275326	3	11	133	4	✗	all	6	point over Q(a)/(a^2 - a + 1)
3.11.275330	3	11	134	2	✗	all	3	empty
3.11.275545	3	11	132	12	✗	all	5	point over Q(a)/(a^2 - a + 1)
3.11.275549	3	11	133	2	✗	all	2	point over Q(a)/(a^2 - a - 1)
3.11.275571	3	11	133	2	✗	all	3	empty
3.11.275575	3	11	134	2	✗	all	5	empty
3.11.275580	3	11	133	2	✗	all	1	point over Q(a)/(a^2 - a - 1)