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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 7,651–7,700

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	birational type ⇅
3.11.220336	3	11	144	1	✓	all but 2,3	rational
3.11.220337	3	11	144	1	✓	all but 2,3,7	rational
3.11.220339	3	11	143	1	✓	all but 2,3,7	point over Q(a)/(a^2 - a + 1)
3.11.220342	3	11	145	2	✓	all but 2,3	rational
3.11.220345	3	11	142	2	✓	all but 2,3	rational
3.11.220346	3	11	147	1	✓	all but 2,3	rational
3.11.220348	3	11	146	1	✓	all but 2,3	rational
3.11.220349	3	11	146	1	✓	all but 2,3	rational
3.11.220350	3	11	144	1	✓	all but 2,3	rational
3.11.220353	3	11	145	1	✓	all but 2,3	point over Q(a)/(a^2 - 2)
3.11.220357	3	11	143	2	✓	all but 2,3	point over Q(a)/(a^2 - a + 1)
3.11.220428	3	11	143	2	✓	all but 2,3	empty
3.11.220438	3	11	147	1	✓	all but 2,3,5,7	rational
3.11.220439	3	11	146	1	✓	all but 2,3,5,7	rational
3.11.220466	3	11	144	1	✓	all but 2,3,5,7	rational
3.11.220467	3	11	143	1	✓	all but 2,3,5,7	point over Q(a)/(a^2 + 1)
3.11.220472	3	11	145	2	✓	all but 2,3	empty
3.11.220474	3	11	144	1	✓	all but 2,3	rational
3.11.220495	3	11	143	2	✓	all but 2,3	empty
3.11.220496	3	11	142	2	✓	all	point over Q(a)/(a^2 + 1)
3.11.220497	3	11	146	2	✓	all but 2	rational over Q(a)/(a^2 + 1)
3.11.220503	3	11	144	1	✓	all but 2,3	empty
3.11.220504	3	11	143	2	✓	all but 2	point over Q(a)/(a^2 + 1)
3.11.220516	3	11	146	2	✓	all but 2,3,5	rational
3.11.220517	3	11	145	2	✓	all but 2	rational
3.11.220518	3	11	145	1	✓	all but 2	rational
3.11.220520	3	11	145	2	✓	all but 2,3,7	rational
3.11.220521	3	11	144	2	✓	all but 2,3	empty
3.11.220523	3	11	144	1	✓	all but 2	rational
3.11.220528	3	11	144	2	✓	all	empty
3.11.220529	3	11	144	1	✓	all but 7	rational
3.11.220530	3	11	144	1	✓	all but 2,3,5,7	rational
3.11.220537	3	11	143	1	✓	all but 2,5	point over Q(a)/(a^2 + 1)
3.11.220539	3	11	144	1	✓	all but 2,3	rational
3.11.220540	3	11	143	1	✓	all but 2,3,5,7	point over Q(a)/(a^3 - a^2 + 1)
3.11.220545	3	11	142	6	✓	all but 2,7	empty
3.11.220546	3	11	141	6	✓	all but 2,3,5	rational
3.11.220547	3	11	145	2	✓	all but 2,3,5,7	rational
3.11.220552	3	11	143	1	✓	all but 2,3	point over Q(a)/(a^2 + 1)
3.11.220575	3	11	144	2	✓	all	rational
3.11.220582	3	11	142	2	✓	all but 2,3	empty
3.11.220583	3	11	141	2	✓	all but 3	empty
3.11.220585	3	11	142	2	✓	all but 2,3,7	empty
3.11.220586	3	11	142	1	✓	all but 2,5	empty
3.11.220601	3	11	142	8	✓	all but 2,3	empty
3.11.220609	3	11	142	1	✓	all but 2,5	empty
3.11.220613	3	11	142	4	✓	all	empty
3.11.220614	3	11	141	8	✓	all	point over Q(a)/(a^2 - a + 1)
3.11.220616	3	11	142	2	✓	all but 2,7	rational over Q(a)/(a^2 - a + 1)
3.11.220618	3	11	139	12	✓	all but 2,3,5	empty