matroid #17 (A variant of #16) — Matroid Correlation Constants

matroid #17 — A variant of #16

n: 23
rank: 13
bases: 439,775
α(M): 63/52 ≈ 1.2115

status: current GF(7) record
discovered by: Yongxi (Aaron) Lin
discovery date: 2026-08
AI use: yes — GPT-5.6 Sol: AI did most of the computations.
submitted by: Yongxi (Aaron) Lin
submitted at: 2026-08-09 17:25:10 UTC

Description (matrix) GF(7)

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

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

Maximizing pair

(21, 22); basis counts at (i, j) = (21, 22):

	`j` ∈ `B`	`j` ∉ `B`
`i` ∈ `B`	128,625	191,100
`i` ∉ `B`	42,875	77,175

Notes

The construction has the block form [C 0 0 u 0 0 C 0 u 0 0 0 C u 0 h h h 0 1]. The inspiration comes from #16.