Best Known (39, 61, s)-Nets in Base 128
(39, 61, 1789)-Net over F128 — Constructive and digital
Digital (39, 61, 1789)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (7, 18, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 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, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 6, 150)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (21, 43, 1489)-net over F128, using
- net defined by OOA [i] based on linear OOA(12843, 1489, F128, 22, 22) (dual of [(1489, 22), 32715, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12843, 16379, F128, 22) (dual of [16379, 16336, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12843, 16379, F128, 22) (dual of [16379, 16336, 23]-code), using
- net defined by OOA [i] based on linear OOA(12843, 1489, F128, 22, 22) (dual of [(1489, 22), 32715, 23]-NRT-code), using
- digital (7, 18, 300)-net over F128, using
(39, 61, 6087)-Net in Base 128 — Constructive
(39, 61, 6087)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- (28, 50, 5958)-net in base 128, using
- net defined by OOA [i] based on OOA(12850, 5958, S128, 22, 22), using
- OA 11-folding and stacking [i] based on OA(12850, 65538, S128, 22), using
- discarding parts of the base [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25641, 65536, F256, 21) (dual of [65536, 65495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [i] based on
- discarding parts of the base [i] based on linear OA(25643, 65538, F256, 22) (dual of [65538, 65495, 23]-code), using
- OA 11-folding and stacking [i] based on OA(12850, 65538, S128, 22), using
- net defined by OOA [i] based on OOA(12850, 5958, S128, 22, 22), using
- digital (0, 11, 129)-net over F128, using
(39, 61, 90299)-Net over F128 — Digital
Digital (39, 61, 90299)-net over F128, using
(39, 61, large)-Net in Base 128 — Upper bound on s
There is no (39, 61, large)-net in base 128, because
- 20 times m-reduction [i] would yield (39, 41, large)-net in base 128, but