Best Known (11, 27, s)-Nets in Base 128
(11, 27, 321)-Net over F128 — Constructive and digital
Digital (11, 27, 321)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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 (3, 19, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (0, 8, 129)-net over F128, using
(11, 27, 384)-Net over F128 — Digital
Digital (11, 27, 384)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12827, 384, F128, 16) (dual of [384, 357, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(12827, 386, F128, 16) (dual of [386, 359, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- linear OA(12826, 382, F128, 16) (dual of [382, 356, 17]-code), using an extension Ce(15) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(12823, 382, F128, 14) (dual of [382, 359, 15]-code), using an extension Ce(13) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(1281, 4, F128, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(12827, 386, F128, 16) (dual of [386, 359, 17]-code), using
(11, 27, 386)-Net in Base 128 — Constructive
(11, 27, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 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
- (3, 19, 257)-net in base 128, using
- 5 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 21, 257)-net over F256, using
- 5 times m-reduction [i] based on (3, 24, 257)-net in base 128, using
- digital (0, 8, 129)-net over F128, using
(11, 27, 383456)-Net in Base 128 — Upper bound on s
There is no (11, 27, 383457)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 784 648029 821317 673956 691235 976303 475402 558774 760700 233700 > 12827 [i]