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Size rank n

Realizability realizable in char 0 realizable in characteristic char set class birational type

92 matroids, showing 1–50

label ▲	rank ⇅	n ⇅	#bases ⇅	#automorphisms ⇅	simple ⇅	char set ⇅	rs dim ⇅	birational type ⇅
3.7.5	3	7	32	48	✓	all	3	rational
3.7.7	3	7	31	4	✓	all	2	rational
3.7.9	3	7	30	12	✓	all	1	rational
3.7.11	3	7	30	8	✓	all	1	rational
3.7.13	3	7	28	168	✓	{2}	-1	empty
3.7.14	3	7	30	240	✗	all	0	rational
3.7.16	3	7	28	16	✗	all	1	rational
3.7.17	3	7	20	720	✗	all	2	rational
3.7.19	3	7	30	144	✓	all	3	rational
3.7.21	3	7	29	4	✓	all	4	rational
3.7.22	3	7	28	6	✓	all	4	rational
3.7.23	3	7	27	72	✓	all	3	rational
3.7.24	3	7	26	48	✗	all	2	rational
3.7.26	3	7	27	24	✗	all	2	rational
3.7.27	3	7	27	4	✗	all	0	rational
3.7.28	3	7	26	4	✗	all	1	rational
3.7.29	3	7	24	12	✗	all	1	rational
3.7.30	3	7	26	16	✗	all	1	rational
3.7.31	3	7	25	4	✗	all	1	rational
3.7.32	3	7	24	8	✗	all	2	rational
3.7.33	3	7	25	48	✗	all	1	rational
3.7.34	3	7	24	48	✗	all	1	rational
3.7.35	3	7	23	8	✗	all	1	rational
3.7.36	3	7	21	8	✗	all	1	rational
3.7.37	3	7	20	48	✗	all	0	rational
3.7.39	3	7	18	72	✗	all	1	rational
3.7.40	3	7	18	8	✗	all	0	rational
3.7.41	3	7	17	6	✗	all	0	rational
3.7.42	3	7	16	24	✗	all	2	rational
3.7.43	3	7	22	144	✗	all	2	rational
3.7.44	3	7	21	36	✗	all	1	rational
3.7.45	3	7	18	144	✗	all	1	rational
3.7.46	3	7	16	48	✗	all	0	rational
3.7.47	3	7	15	12	✗	all	0	rational
3.7.48	3	7	10	240	✗	all	0	rational
3.7.50	3	7	24	48	✓	all	2	rational
3.7.51	3	7	20	240	✗	all	0	rational
3.7.52	3	7	23	24	✗	all	1	rational
3.7.53	3	7	22	8	✗	all	0	rational
3.7.54	3	7	21	24	✗	all	0	rational
3.7.55	3	7	18	24	✗	all	2	rational
3.7.56	3	7	21	16	✗	all	0	rational
3.7.57	3	7	20	16	✗	all	0	rational
3.7.58	3	7	19	8	✗	all	0	rational
3.7.59	3	7	16	16	✗	all	0	rational
3.7.60	3	7	16	48	✗	all	1	rational
3.7.61	3	7	15	12	✗	all	0	rational
3.7.62	3	7	12	48	✗	all	3	rational
3.7.63	3	7	19	24	✗	all	0	rational
3.7.64	3	7	18	12	✗	all	2	rational