# Longest constrained sequences

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The numbers in square brackets show (what we know of) the length of the longest sequence of discrepancy 2 satisfying the given constraints exactly. The notation $a=b$ is shorthand for $T_a(x) = T_b(x)$, and $a=-b$ for $T_a(x) = -T_b(x)$.

1 = +2 : [170]
1 = -2 : [>=974]
1 = -2,  1 = +3 : [188]
1 = -2,  1 = -3 : [470]
1 = -2,  1 = +5 : [356]
1 = -2,  1 = -5 : [>=974]
1 = -2,  1 = -5,  1 =  +7 : [>=566]
1 = -2,  1 = -5,  1 =  -7 : [284]
1 = -2,  1 = -5, 11 = -13 : [>=974]
1 = -2,  1 = -5, 11 = -13, 17 = -19 : [974]
1 = -2,  1 = -5, 11 = -13, 17 = -19, 23 = +29 : [974]
1 = -2,  1 = -5, 11 = -13, 17 = -19, 23 = +29, 23 = -31 : [854]
1 = +3 : [188]
1 = -3 : [>=575]
1 = -3,  1 = -5 : [>=476]
1 = -3,  1 = +5 : [>=376]
1 = -3,  2 = +5 : [>=506]
1 = -3,  2 = +5,  1 = -11 : [506]
1 = +32 : [>=417]
2 = +3 : [>=549*]
2 = -3 : [>=641]

• Asterisk means that a depth-first search with a little look-ahead showed that the maximum is finite, but the actual maximum may be slightly above that shown.