Best Known (21, 21+12, s)-Nets in Base 128
(21, 21+12, 3010)-Net over F128 — Constructive and digital
Digital (21, 33, 3010)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 279)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 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
- digital (1, 7, 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 (0, 3, 129)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (11, 23, 2731)-net over F128, using
- net defined by OOA [i] based on linear OOA(12823, 2731, F128, 12, 12) (dual of [(2731, 12), 32749, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(12823, 16386, F128, 12) (dual of [16386, 16363, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12821, 16384, F128, 11) (dual of [16384, 16363, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(12823, 16386, F128, 12) (dual of [16386, 16363, 13]-code), using
- net defined by OOA [i] based on linear OOA(12823, 2731, F128, 12, 12) (dual of [(2731, 12), 32749, 13]-NRT-code), using
- digital (4, 10, 279)-net over F128, using
(21, 21+12, 11052)-Net in Base 128 — Constructive
(21, 33, 11052)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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
- (15, 27, 10923)-net in base 128, using
- net defined by OOA [i] based on OOA(12827, 10923, S128, 12, 12), using
- OA 6-folding and stacking [i] based on OA(12827, 65538, S128, 12), using
- discarding parts of the base [i] based on linear OA(25623, 65538, F256, 12) (dual of [65538, 65515, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(25623, 65536, F256, 12) (dual of [65536, 65513, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(11) ⊂ Ce(10) [i] based on
- discarding parts of the base [i] based on linear OA(25623, 65538, F256, 12) (dual of [65538, 65515, 13]-code), using
- OA 6-folding and stacking [i] based on OA(12827, 65538, S128, 12), using
- net defined by OOA [i] based on OOA(12827, 10923, S128, 12, 12), using
- digital (0, 6, 129)-net over F128, using
(21, 21+12, 81072)-Net over F128 — Digital
Digital (21, 33, 81072)-net over F128, using
(21, 21+12, large)-Net in Base 128 — Upper bound on s
There is no (21, 33, large)-net in base 128, because
- 10 times m-reduction [i] would yield (21, 23, large)-net in base 128, but