matroid #10 (A variant of #6) — Matroid Correlation Constants

matroid #10 — A variant of #6

n: 26
rank: 9
bases: 1,520,989
α(M): 561630/487297 ≈ 1.1525

status: superseded — held the GF(7) record until beaten
discovered by: Yongxi (Aaron) Lin
discovery date: 2026-08
AI use: yes — ChatGPT 5.6 Sol: AI found it by itself by responding to my prompt: "try to construct Matroids for GF(n) to beat the record"
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-09 05:45:32 UTC

Description (matrix) GF(7)

[[5,3,2,4,5,3,2,3,3,3,2,4,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
 [1,0,1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
 [4,1,6,1,6,6,2,1,0,4,4,4,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
 [5,2,2,3,0,1,3,1,4,1,4,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
 [0,0,0,0,0,0,0,0,0,0,0,0,5,3,2,4,5,3,2,3,3,3,2,4,1,0],
 [0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,1,1,1,0,1,1,1,1,0,0],
 [0,0,0,0,0,0,0,0,0,0,0,0,4,1,6,1,6,6,2,1,0,4,4,4,0,0],
 [0,0,0,0,0,0,0,0,0,0,0,0,5,2,2,3,0,1,3,1,4,1,4,2,0,0],
 [0,0,0,0,6,4,5,2,1,0,2,5,0,0,0,0,4,3,3,0,2,2,5,1,5,1]]

The full basis list is too large to store; recompute it from the description above.

Maximizing pair

(24, 25); basis counts at (i, j) = (24, 25):

	`j` ∈ `B`	`j` ∉ `B`
`i` ∈ `B`	174,086	487,297
`i` ∉ `B`	203,401	656,205

Notes

Only the last row of the matrix is different the one in #6.