matroid #13 ([C 0 u 0; 0 C u 0; h h 0 1]) — Matroid Correlation Constants

matroid #13 — [C 0 u 0; 0 C u 0; h h 0 1]

n: 26
rank: 9
bases: 1,131,928
α(M): 55752/48391 ≈ 1.1521

status: superseded — held the GF(4) record until beaten
discovered by: Yongxi (Aaron) Lin
discovery date: 2026-08
AI use: yes — GPT-5.6 Sol: AI uses the matrix that appears in #12.
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-09 08:11:58 UTC

Description (matrix) GF(4)

[[1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,0],
 [0,1,0,0,1,0,[1,1],0,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,[1,1],0],
 [0,0,1,0,0,1,[1,1],[1,1],1,[0,1],1,[0,1],0,0,0,0,0,0,0,0,0,0,0,0,1,0],
 [0,0,0,1,1,0,1,1,1,[0,1],0,0,0,0,0,0,0,0,0,0,0,0,0,0,[1,1],0],
 [0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,1,1,1,0,1,0,1,1,0],
 [0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,0,[1,1],0,1,0,1,1,[1,1],0],
 [0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,1,[1,1],[1,1],1,[0,1],1,[0,1],1,0],
 [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,1,1,1,[0,1],0,0,[1,1],0],
 [0,0,0,0,1,[0,1],[0,1],[1,1],[0,1],0,0,[1,1],0,0,0,0,1,[0,1],[0,1],[1,1],[0,1],0,0,[1,1],0,1]]

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`	139,840	387,128
`i` ∉ `B`	144,400	460,560

Notes

The construction has the form [C 0 u 0; 0 C u 0; h h 0 1] with a rank-4, 12-column seed C. u = [1,3,1,3] h = [1,2,2,3,2,0,0,3]