Best Known (50, 50+28, s)-Nets in Base 128
(50, 50+28, 1470)-Net over F128 — Constructive and digital
Digital (50, 78, 1470)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (9, 23, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (1, 15, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 8, 150)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (27, 55, 1170)-net over F128, using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(12855, 16384, F128, 28) (dual of [16384, 16329, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(12855, 16380, F128, 28) (dual of [16380, 16325, 29]-code), using
- net defined by OOA [i] based on linear OOA(12855, 1170, F128, 28, 28) (dual of [(1170, 28), 32705, 29]-NRT-code), using
- digital (9, 23, 300)-net over F128, using
(50, 50+28, 4831)-Net in Base 128 — Constructive
(50, 78, 4831)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- (35, 63, 4681)-net in base 128, using
- net defined by OOA [i] based on OOA(12863, 4681, S128, 28, 28), using
- OA 14-folding and stacking [i] based on OA(12863, 65534, S128, 28), using
- discarding factors based on OA(12863, 65538, S128, 28), using
- discarding parts of the base [i] based on linear OA(25655, 65538, F256, 28) (dual of [65538, 65483, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(26) [i] based on
- discarding parts of the base [i] based on linear OA(25655, 65538, F256, 28) (dual of [65538, 65483, 29]-code), using
- discarding factors based on OA(12863, 65538, S128, 28), using
- OA 14-folding and stacking [i] based on OA(12863, 65534, S128, 28), using
- net defined by OOA [i] based on OOA(12863, 4681, S128, 28, 28), using
- digital (1, 15, 150)-net over F128, using
(50, 50+28, 105234)-Net over F128 — Digital
Digital (50, 78, 105234)-net over F128, using
(50, 50+28, large)-Net in Base 128 — Upper bound on s
There is no (50, 78, large)-net in base 128, because
- 26 times m-reduction [i] would yield (50, 52, large)-net in base 128, but