Best Known (155−14, 155, s)-Nets in Base 2
(155−14, 155, 599189)-Net over F2 — Constructive and digital
Digital (141, 155, 599189)-net over F2, using
- net defined by OOA [i] based on linear OOA(2155, 599189, F2, 14, 14) (dual of [(599189, 14), 8388491, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2155, 4194323, F2, 14) (dual of [4194323, 4194168, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-code), using
- 1 times truncation [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2155, 4194323, F2, 14) (dual of [4194323, 4194168, 15]-code), using
(155−14, 155, 838865)-Net over F2 — Digital
Digital (141, 155, 838865)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2155, 838865, F2, 5, 14) (dual of [(838865, 5), 4194170, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2155, 4194325, F2, 14) (dual of [4194325, 4194170, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-code), using
- 1 times truncation [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
- dual of repetition code with length 24 [i]
- linear OA(21, 24, F2, 1) (dual of [24, 23, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(14) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-code), using
- OOA 5-folding [i] based on linear OA(2155, 4194325, F2, 14) (dual of [4194325, 4194170, 15]-code), using
(155−14, 155, large)-Net in Base 2 — Upper bound on s
There is no (141, 155, large)-net in base 2, because
- 12 times m-reduction [i] would yield (141, 143, large)-net in base 2, but