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Catalog of Isomorphism Classes of Oriented Matroids

The following table shows the number of non-degenerate (uniform) isomorphism classes of oriented matroids (where card is the cardinality of a simple representative). Data can be accessed by clicking on the corresponding number (if available):

All

Non-degenerate (Uniform)

	card = 2	card = 3	card = 4	card = 5	card = 6	card = 7	card = 8	card = 9	card = 10
rank = 2	1	1	1	1	1	1	1	1	1
rank = 3 (dim = 2)		1	1	1	4	11	135	4 382	312 356
rank = 4 (dim = 3)			1	1	1	11	2 628	9 276 595	unknown
rank = 5 (dim = 4)				1	1	1	135	9 276 595	unknown
rank = 6 (dim = 5)					1	1	1	4 382	unknown
rank = 7 (dim = 6)						1	1	1	312 356
rank = 8 (dim = 7)							1	1	1
rank = 9 (dim = 8)								1	1
rank = 10 (dim = 9)									1

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