matroid #5 — HSW spike construction at q = 4
- n
- 18
- rank
- 5
- bases
- 3,392
- α(M)
- 8/7 ≈ 1.1429
Description (matrix) GF(4)
[[1,0,0,1,[0,1],[1,1],0,1,[0,1],[1,1],0,1,[0,1],[1,1],0,1,[0,1],[1,1]], [0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,1,1,1,1,0,0,0,0], [0,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1]]
show all 3,392 bases
[[0,1,2,6,10], [0,1,3,6,10], [1,2,3,6,10], [0,1,4,6,10], [1,2,4,6,10], [1,3,4,6,10], [0,1,5,6,10], [1,2,5,6,10], [1,3,5,6,10], [1,4,5,6,10], [0,1,2,7,10], [0,1,3,7,10], [1,2,3,7,10], [0,1,4,7,10], [1,2,4,7,10], [1,3,4,7,10], [0,1,5,7,10], [1,2,5,7,10], [1,3,5,7,10], [1,4,5,7,10], [1,2,6,7,10], [1,3,6,7,10], [1,4,6,7,10], [1,5,6,7,10], [0,1,2,8,10], [0,1,3,8,10], [1,2,3,8,10], [0,1,4,8,10], [1,2,4,8,10], [1,3,4,8,10], [0,1,5,8,10], [1,2,5,8,10], [1,3,5,8,10], [1,4,5,8,10], [1,2,6,8,10], [1,3,6,8,10], [1,4,6,8,10], [1,5,6,8,10], [1,2,7,8,10], [1,3,7,8,10], [1,4,7,8,10], [1,5,7,8,10], [0,1,2,9,10], [0,1,3,9,10], [1,2,3,9,10], [0,1,4,9,10], [1,2,4,9,10], [1,3,4,9,10], [0,1,5,9,10], [1,2,5,9,10], [1,3,5,9,10], [1,4,5,9,10], [1,2,6,9,10], [1,3,6,9,10], [1,4,6,9,10], [1,5,6,9,10], [1,2,7,9,10], [1,3,7,9,10], [1,4,7,9,10], [1,5,7,9,10], [1,2,8,9,10], [1,3,8,9,10], [1,4,8,9,10], [1,5,8,9,10], [0,1,2,6,11], [0,1,3,6,11], [1,2,3,6,11], [0,1,4,6,11], [1,2,4,6,11], [1,3,4,6,11], [0,1,5,6,11], [1,2,5,6,11], [1,3,5,6,11], [1,4,5,6,11], [0,1,2,7,11], [0,1,3,7,11], [1,2,3,7,11], [0,1,4,7,11], [1,2,4,7,11], [1,3,4,7,11], [0,1,5,7,11], [1,2,5,7,11], [1,3,5,7,11], [1,4,5,7,11], [1,2,6,7,11], [1,3,6,7,11], [1,4,6,7,11], [1,5,6,7,11], [0,1,2,8,11], [0,1,3,8,11], [1,2,3,8,11], [0,1,4,8,11], [1,2,4,8,11], [1,3,4,8,11], [0,1,5,8,11], [1,2,5,8,11], [1,3,5,8,11], [1,4,5,8,11], [1,2,6,8,11], [1,3,6,8,11], [1,4,6,8,11], [1,5,6,8,11], [1,2,7,8,11], [1,3,7,8,11], [1,4,7,8,11], [1,5,7,8,11], [0,1,2,9,11], [0,1,3,9,11], [1,2,3,9,11], [0,1,4,9,11], [1,2,4,9,11], [1,3,4,9,11], [0,1,5,9,11], [1,2,5,9,11], [1,3,5,9,11], [1,4,5,9,11], [1,2,6,9,11], [1,3,6,9,11], [1,4,6,9,11], [1,5,6,9,11], [1,2,7,9,11], [1,3,7,9,11], [1,4,7,9,11], [1,5,7,9,11], [1,2,8,9,11], [1,3,8,9,11], [1,4,8,9,11], [1,5,8,9,11], [1,2,6,10,11], [1,3,6,10,11], [1,4,6,10,11], [1,5,6,10,11], [1,2,7,10,11], [1,3,7,10,11], [1,4,7,10,11], [1,5,7,10,11], [1,2,8,10,11], [1,3,8,10,11], [1,4,8,10,11], [1,5,8,10,11], [1,2,9,10,11], [1,3,9,10,11], [1,4,9,10,11], [1,5,9,10,11], [0,1,2,6,12], [0,1,3,6,12], [1,2,3,6,12], [0,1,4,6,12], [1,2,4,6,12], [1,3,4,6,12], [0,1,5,6,12], [1,2,5,6,12], [1,3,5,6,12], [1,4,5,6,12], [0,1,2,7,12], [0,1,3,7,12], [1,2,3,7,12], [0,1,4,7,12], [1,2,4,7,12], [1,3,4,7,12], [0,1,5,7,12], [1,2,5,7,12], [1,3,5,7,12], [1,4,5,7,12], [1,2,6,7,12], [1,3,6,7,12], [1,4,6,7,12], [1,5,6,7,12], [0,1,2,8,12], [0,1,3,8,12], [1,2,3,8,12], [0,1,4,8,12], [1,2,4,8,12], [1,3,4,8,12], [0,1,5,8,12], [1,2,5,8,12], [1,3,5,8,12], [1,4,5,8,12], [1,2,6,8,12], [1,3,6,8,12], [1,4,6,8,12], [1,5,6,8,12], [1,2,7,8,12], [1,3,7,8,12], [1,4,7,8,12], [1,5,7,8,12], [0,1,2,9,12], [0,1,3,9,12], [1,2,3,9,12], [0,1,4,9,12], [1,2,4,9,12], [1,3,4,9,12], [0,1,5,9,12], [1,2,5,9,12], [1,3,5,9,12], [1,4,5,9,12], [1,2,6,9,12], [1,3,6,9,12], [1,4,6,9,12], [1,5,6,9,12], [1,2,7,9,12], [1,3,7,9,12], [1,4,7,9,12], [1,5,7,9,12], [1,2,8,9,12], [1,3,8,9,12], [1,4,8,9,12], [1,5,8,9,12], [1,2,6,10,12], [1,3,6,10,12], [1,4,6,10,12], [1,5,6,10,12], [1,2,7,10,12], [1,3,7,10,12], [1,4,7,10,12], [1,5,7,10,12], [1,2,8,10,12], [1,3,8,10,12], [1,4,8,10,12], [1,5,8,10,12], [1,2,9,10,12], [1,3,9,10,12], [1,4,9,10,12], [1,5,9,10,12], [1,2,6,11,12], [1,3,6,11,12], [1,4,6,11,12], [1,5,6,11,12], [1,2,7,11,12], [1,3,7,11,12], [1,4,7,11,12], [1,5,7,11,12], [1,2,8,11,12], [1,3,8,11,12], [1,4,8,11,12], [1,5,8,11,12], [1,2,9,11,12], [1,3,9,11,12], [1,4,9,11,12], [1,5,9,11,12], [0,1,2,6,13], [0,1,3,6,13], [1,2,3,6,13], [0,1,4,6,13], [1,2,4,6,13], [1,3,4,6,13], [0,1,5,6,13], [1,2,5,6,13], [1,3,5,6,13], [1,4,5,6,13], [0,1,2,7,13], [0,1,3,7,13], [1,2,3,7,13], [0,1,4,7,13], [1,2,4,7,13], [1,3,4,7,13], [0,1,5,7,13], [1,2,5,7,13], [1,3,5,7,13], [1,4,5,7,13], [1,2,6,7,13], [1,3,6,7,13], [1,4,6,7,13], [1,5,6,7,13], [0,1,2,8,13], [0,1,3,8,13], [1,2,3,8,13], [0,1,4,8,13], [1,2,4,8,13], [1,3,4,8,13], [0,1,5,8,13], [1,2,5,8,13], [1,3,5,8,13], [1,4,5,8,13], [1,2,6,8,13], [1,3,6,8,13], [1,4,6,8,13], [1,5,6,8,13], [1,2,7,8,13], [1,3,7,8,13], [1,4,7,8,13], [1,5,7,8,13], [0,1,2,9,13], [0,1,3,9,13], [1,2,3,9,13], [0,1,4,9,13], [1,2,4,9,13], [1,3,4,9,13], [0,1,5,9,13], [1,2,5,9,13], [1,3,5,9,13], [1,4,5,9,13], [1,2,6,9,13], [1,3,6,9,13], [1,4,6,9,13], [1,5,6,9,13], [1,2,7,9,13], [1,3,7,9,13], [1,4,7,9,13], [1,5,7,9,13], [1,2,8,9,13], [1,3,8,9,13], [1,4,8,9,13], [1,5,8,9,13], [1,2,6,10,13], [1,3,6,10,13], [1,4,6,10,13], [1,5,6,10,13], [1,2,7,10,13], [1,3,7,10,13], [1,4,7,10,13], [1,5,7,10,13], [1,2,8,10,13], [1,3,8,10,13], [1,4,8,10,13], [1,5,8,10,13], [1,2,9,10,13], [1,3,9,10,13], [1,4,9,10,13], [1,5,9,10,13], [1,2,6,11,13], [1,3,6,11,13], [1,4,6,11,13], [1,5,6,11,13], [1,2,7,11,13], [1,3,7,11,13], [1,4,7,11,13], [1,5,7,11,13], [1,2,8,11,13], [1,3,8,11,13], [1,4,8,11,13], [1,5,8,11,13], [1,2,9,11,13], [1,3,9,11,13], [1,4,9,11,13], [1,5,9,11,13], [1,2,6,12,13], [1,3,6,12,13], [1,4,6,12,13], [1,5,6,12,13], [1,2,7,12,13], [1,3,7,12,13], [1,4,7,12,13], [1,5,7,12,13], [1,2,8,12,13], [1,3,8,12,13], [1,4,8,12,13], [1,5,8,12,13], [1,2,9,12,13], [1,3,9,12,13], [1,4,9,12,13], [1,5,9,12,13], [0,1,2,6,14], [0,1,3,6,14], [1,2,3,6,14], [0,1,4,6,14], [1,2,4,6,14], [1,3,4,6,14], [0,1,5,6,14], [1,2,5,6,14], [1,3,5,6,14], [1,4,5,6,14], [0,1,2,7,14], [0,1,3,7,14], [1,2,3,7,14], [0,1,4,7,14], [1,2,4,7,14], [1,3,4,7,14], [0,1,5,7,14], [1,2,5,7,14], [1,3,5,7,14], [1,4,5,7,14], [1,2,6,7,14], [1,3,6,7,14], [1,4,6,7,14], [1,5,6,7,14], [0,1,2,8,14], [0,1,3,8,14], [1,2,3,8,14], [0,1,4,8,14], [1,2,4,8,14], [1,3,4,8,14], [0,1,5,8,14], [1,2,5,8,14], [1,3,5,8,14], [1,4,5,8,14], [1,2,6,8,14], [1,3,6,8,14], [1,4,6,8,14], [1,5,6,8,14], [1,2,7,8,14], [1,3,7,8,14], [1,4,7,8,14], [1,5,7,8,14], [0,1,2,9,14], [0,1,3,9,14], [1,2,3,9,14], [0,1,4,9,14], [1,2,4,9,14], [1,3,4,9,14], [0,1,5,9,14], [1,2,5,9,14], [1,3,5,9,14], [1,4,5,9,14], [1,2,6,9,14], [1,3,6,9,14], [1,4,6,9,14], [1,5,6,9,14], [1,2,7,9,14], [1,3,7,9,14], [1,4,7,9,14], [1,5,7,9,14], [1,2,8,9,14], [1,3,8,9,14], [1,4,8,9,14], [1,5,8,9,14], [0,1,2,10,14], [0,1,3,10,14], [1,2,3,10,14], [0,1,4,10,14], [1,2,4,10,14], [1,3,4,10,14], [0,1,5,10,14], [1,2,5,10,14], [1,3,5,10,14], [1,4,5,10,14], [0,1,6,10,14], [0,2,6,10,14], [0,3,6,10,14], [1,3,6,10,14], [2,3,6,10,14], [0,4,6,10,14], [1,4,6,10,14], [2,4,6,10,14], [3,4,6,10,14], [0,5,6,10,14], [1,5,6,10,14], [2,5,6,10,14], [3,5,6,10,14], [4,5,6,10,14], [0,1,7,10,14], [0,2,7,10,14], [1,2,7,10,14], [0,3,7,10,14], [2,3,7,10,14], [0,4,7,10,14], [1,4,7,10,14], [2,4,7,10,14], [3,4,7,10,14], [0,5,7,10,14], [1,5,7,10,14], [2,5,7,10,14], [3,5,7,10,14], [4,5,7,10,14], [1,6,7,10,14], [2,6,7,10,14], [3,6,7,10,14], [4,6,7,10,14], [5,6,7,10,14], [0,1,8,10,14], [0,2,8,10,14], [1,2,8,10,14], [0,3,8,10,14], [1,3,8,10,14], [2,3,8,10,14], [0,4,8,10,14], [2,4,8,10,14], [3,4,8,10,14], [0,5,8,10,14], [1,5,8,10,14], [2,5,8,10,14], [3,5,8,10,14], [4,5,8,10,14], [1,6,8,10,14], [2,6,8,10,14], [3,6,8,10,14], [4,6,8,10,14], [5,6,8,10,14], [1,7,8,10,14], [2,7,8,10,14], [3,7,8,10,14], [4,7,8,10,14], [5,7,8,10,14], [0,1,9,10,14], [0,2,9,10,14], [1,2,9,10,14], [0,3,9,10,14], [1,3,9,10,14], [2,3,9,10,14], [0,4,9,10,14], [1,4,9,10,14], [2,4,9,10,14], [3,4,9,10,14], [0,5,9,10,14], [2,5,9,10,14], [3,5,9,10,14], [4,5,9,10,14], [1,6,9,10,14], [2,6,9,10,14], [3,6,9,10,14], [4,6,9,10,14], [5,6,9,10,14], [1,7,9,10,14], [2,7,9,10,14], [3,7,9,10,14], [4,7,9,10,14], [5,7,9,10,14], [1,8,9,10,14], [2,8,9,10,14], [3,8,9,10,14], [4,8,9,10,14], [5,8,9,10,14], [0,1,2,11,14], [0,1,3,11,14], [1,2,3,11,14], [0,1,4,11,14], [1,2,4,11,14], [1,3,4,11,14], [0,1,5,11,14], [1,2,5,11,14], [1,3,5,11,14], [1,4,5,11,14], [0,1,6,11,14], [0,2,6,11,14], [1,2,6,11,14], [0,3,6,11,14], [2,3,6,11,14], [0,4,6,11,14], [1,4,6,11,14], [2,4,6,11,14], [3,4,6,11,14], [0,5,6,11,14], [1,5,6,11,14], [2,5,6,11,14], [3,5,6,11,14], [4,5,6,11,14], [0,1,7,11,14], [0,2,7,11,14], [0,3,7,11,14], [1,3,7,11,14], [2,3,7,11,14], [0,4,7,11,14], [1,4,7,11,14], [2,4,7,11,14], [3,4,7,11,14], [0,5,7,11,14], [1,5,7,11,14], [2,5,7,11,14], [3,5,7,11,14], [4,5,7,11,14], [1,6,7,11,14], [2,6,7,11,14], 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[3,8,11,13,17], [4,8,11,13,17], [5,8,11,13,17], [1,9,11,13,17], [2,9,11,13,17], [3,9,11,13,17], [4,9,11,13,17], [5,9,11,13,17], [1,2,12,13,17], [1,3,12,13,17], [1,4,12,13,17], [1,5,12,13,17], [1,6,12,13,17], [2,6,12,13,17], [3,6,12,13,17], [4,6,12,13,17], [5,6,12,13,17], [1,7,12,13,17], [2,7,12,13,17], [3,7,12,13,17], [4,7,12,13,17], [5,7,12,13,17], [1,8,12,13,17], [2,8,12,13,17], [3,8,12,13,17], [4,8,12,13,17], [5,8,12,13,17], [1,9,12,13,17], [2,9,12,13,17], [3,9,12,13,17], [4,9,12,13,17], [5,9,12,13,17], [1,2,6,14,17], [1,3,6,14,17], [1,4,6,14,17], [1,5,6,14,17], [1,2,7,14,17], [1,3,7,14,17], [1,4,7,14,17], [1,5,7,14,17], [1,2,8,14,17], [1,3,8,14,17], [1,4,8,14,17], [1,5,8,14,17], [1,2,9,14,17], [1,3,9,14,17], [1,4,9,14,17], [1,5,9,14,17], [1,2,10,14,17], [1,3,10,14,17], [1,4,10,14,17], [1,5,10,14,17], [1,6,10,14,17], [2,6,10,14,17], [3,6,10,14,17], [4,6,10,14,17], [5,6,10,14,17], [1,7,10,14,17], [2,7,10,14,17], [3,7,10,14,17], [4,7,10,14,17], [5,7,10,14,17], [1,8,10,14,17], [2,8,10,14,17], [3,8,10,14,17], [4,8,10,14,17], [5,8,10,14,17], [1,9,10,14,17], [2,9,10,14,17], [3,9,10,14,17], [4,9,10,14,17], [5,9,10,14,17], [1,2,11,14,17], [1,3,11,14,17], [1,4,11,14,17], [1,5,11,14,17], [1,6,11,14,17], [2,6,11,14,17], [3,6,11,14,17], [4,6,11,14,17], [5,6,11,14,17], [1,7,11,14,17], [2,7,11,14,17], [3,7,11,14,17], [4,7,11,14,17], [5,7,11,14,17], [1,8,11,14,17], [2,8,11,14,17], [3,8,11,14,17], [4,8,11,14,17], [5,8,11,14,17], [1,9,11,14,17], [2,9,11,14,17], [3,9,11,14,17], [4,9,11,14,17], [5,9,11,14,17], [1,2,12,14,17], [1,3,12,14,17], [1,4,12,14,17], [1,5,12,14,17], [1,6,12,14,17], [2,6,12,14,17], [3,6,12,14,17], [4,6,12,14,17], [5,6,12,14,17], [1,7,12,14,17], [2,7,12,14,17], [3,7,12,14,17], [4,7,12,14,17], [5,7,12,14,17], [1,8,12,14,17], [2,8,12,14,17], [3,8,12,14,17], [4,8,12,14,17], [5,8,12,14,17], [1,9,12,14,17], [2,9,12,14,17], [3,9,12,14,17], [4,9,12,14,17], [5,9,12,14,17], [1,2,13,14,17], [1,3,13,14,17], [1,4,13,14,17], [1,5,13,14,17], [1,6,13,14,17], [2,6,13,14,17], [3,6,13,14,17], [4,6,13,14,17], [5,6,13,14,17], [1,7,13,14,17], [2,7,13,14,17], [3,7,13,14,17], [4,7,13,14,17], [5,7,13,14,17], [1,8,13,14,17], [2,8,13,14,17], [3,8,13,14,17], [4,8,13,14,17], [5,8,13,14,17], [1,9,13,14,17], [2,9,13,14,17], [3,9,13,14,17], [4,9,13,14,17], [5,9,13,14,17], [1,2,6,15,17], [1,3,6,15,17], [1,4,6,15,17], [1,5,6,15,17], [1,2,7,15,17], [1,3,7,15,17], [1,4,7,15,17], [1,5,7,15,17], [1,2,8,15,17], [1,3,8,15,17], [1,4,8,15,17], [1,5,8,15,17], [1,2,9,15,17], [1,3,9,15,17], [1,4,9,15,17], [1,5,9,15,17], [1,2,10,15,17], [1,3,10,15,17], [1,4,10,15,17], [1,5,10,15,17], [1,6,10,15,17], [2,6,10,15,17], [3,6,10,15,17], [4,6,10,15,17], [5,6,10,15,17], [1,7,10,15,17], [2,7,10,15,17], [3,7,10,15,17], [4,7,10,15,17], [5,7,10,15,17], [1,8,10,15,17], [2,8,10,15,17], [3,8,10,15,17], [4,8,10,15,17], [5,8,10,15,17], [1,9,10,15,17], [2,9,10,15,17], [3,9,10,15,17], [4,9,10,15,17], [5,9,10,15,17], [1,2,11,15,17], [1,3,11,15,17], [1,4,11,15,17], [1,5,11,15,17], [1,6,11,15,17], [2,6,11,15,17], [3,6,11,15,17], [4,6,11,15,17], [5,6,11,15,17], [1,7,11,15,17], [2,7,11,15,17], [3,7,11,15,17], [4,7,11,15,17], [5,7,11,15,17], [1,8,11,15,17], [2,8,11,15,17], [3,8,11,15,17], [4,8,11,15,17], [5,8,11,15,17], [1,9,11,15,17], [2,9,11,15,17], [3,9,11,15,17], [4,9,11,15,17], [5,9,11,15,17], [1,2,12,15,17], [1,3,12,15,17], [1,4,12,15,17], [1,5,12,15,17], [1,6,12,15,17], [2,6,12,15,17], [3,6,12,15,17], [4,6,12,15,17], [5,6,12,15,17], [1,7,12,15,17], [2,7,12,15,17], [3,7,12,15,17], [4,7,12,15,17], [5,7,12,15,17], [1,8,12,15,17], [2,8,12,15,17], [3,8,12,15,17], [4,8,12,15,17], [5,8,12,15,17], [1,9,12,15,17], [2,9,12,15,17], [3,9,12,15,17], [4,9,12,15,17], [5,9,12,15,17], [1,2,13,15,17], [1,3,13,15,17], [1,4,13,15,17], [1,5,13,15,17], [1,6,13,15,17], [2,6,13,15,17], [3,6,13,15,17], [4,6,13,15,17], [5,6,13,15,17], [1,7,13,15,17], [2,7,13,15,17], [3,7,13,15,17], [4,7,13,15,17], [5,7,13,15,17], [1,8,13,15,17], [2,8,13,15,17], [3,8,13,15,17], [4,8,13,15,17], [5,8,13,15,17], [1,9,13,15,17], [2,9,13,15,17], [3,9,13,15,17], [4,9,13,15,17], [5,9,13,15,17], [1,2,6,16,17], [1,3,6,16,17], [1,4,6,16,17], [1,5,6,16,17], [1,2,7,16,17], [1,3,7,16,17], [1,4,7,16,17], [1,5,7,16,17], [1,2,8,16,17], [1,3,8,16,17], [1,4,8,16,17], [1,5,8,16,17], [1,2,9,16,17], [1,3,9,16,17], [1,4,9,16,17], [1,5,9,16,17], [1,2,10,16,17], [1,3,10,16,17], [1,4,10,16,17], [1,5,10,16,17], [1,6,10,16,17], [2,6,10,16,17], [3,6,10,16,17], [4,6,10,16,17], [5,6,10,16,17], [1,7,10,16,17], [2,7,10,16,17], [3,7,10,16,17], [4,7,10,16,17], [5,7,10,16,17], [1,8,10,16,17], [2,8,10,16,17], [3,8,10,16,17], [4,8,10,16,17], [5,8,10,16,17], [1,9,10,16,17], [2,9,10,16,17], [3,9,10,16,17], [4,9,10,16,17], [5,9,10,16,17], [1,2,11,16,17], [1,3,11,16,17], [1,4,11,16,17], [1,5,11,16,17], [1,6,11,16,17], [2,6,11,16,17], [3,6,11,16,17], [4,6,11,16,17], [5,6,11,16,17], [1,7,11,16,17], [2,7,11,16,17], [3,7,11,16,17], [4,7,11,16,17], [5,7,11,16,17], [1,8,11,16,17], [2,8,11,16,17], [3,8,11,16,17], [4,8,11,16,17], [5,8,11,16,17], [1,9,11,16,17], [2,9,11,16,17], [3,9,11,16,17], [4,9,11,16,17], [5,9,11,16,17], [1,2,12,16,17], [1,3,12,16,17], [1,4,12,16,17], [1,5,12,16,17], [1,6,12,16,17], [2,6,12,16,17], [3,6,12,16,17], [4,6,12,16,17], [5,6,12,16,17], [1,7,12,16,17], [2,7,12,16,17], [3,7,12,16,17], [4,7,12,16,17], [5,7,12,16,17], [1,8,12,16,17], [2,8,12,16,17], [3,8,12,16,17], [4,8,12,16,17], [5,8,12,16,17], [1,9,12,16,17], [2,9,12,16,17], [3,9,12,16,17], [4,9,12,16,17], [5,9,12,16,17], [1,2,13,16,17], [1,3,13,16,17], [1,4,13,16,17], [1,5,13,16,17], [1,6,13,16,17], [2,6,13,16,17], [3,6,13,16,17], [4,6,13,16,17], [5,6,13,16,17], [1,7,13,16,17], [2,7,13,16,17], [3,7,13,16,17], [4,7,13,16,17], [5,7,13,16,17], [1,8,13,16,17], [2,8,13,16,17], [3,8,13,16,17], [4,8,13,16,17], [5,8,13,16,17], [1,9,13,16,17], [2,9,13,16,17], [3,9,13,16,17], [4,9,13,16,17], [5,9,13,16,17]]
Maximizing pair
(0, 1); basis counts at (i, j) = (0, 1):
| j ∈ B | j ∉ B | |
|---|---|---|
| i ∈ B | 256 | 256 |
| i ∉ B | 1,344 | 1,536 |
Notes
The Huh-Schroter-Wang spike construction (Correlation bounds for fields and matroids, arXiv:1806.02675, Definition 19) instantiated over the non-prime field GF(4): tip e1, the vector e2+e3+e4+e5, and k*e1+e_m for m=2..5 and all k in GF(4) (entries in the Conway basis, a = [0,1]). The paper fixes a prime p, but the Section 5 counting argument applies verbatim over any finite field; the counts (256, 1536, 256, 1344) match its formulas at q=4. Assembled and verified for this site, August 2026, with AI assistance (Claude Fable 5 via Claude Code).
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