Best Known (7, 17, s)-Nets in Base 128
(7, 17, 300)-Net over F128 — Constructive and digital
Digital (7, 17, 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, 11, 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
(7, 17, 386)-Net in Base 128 — Constructive
(7, 17, 386)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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
- (2, 12, 257)-net in base 128, using
- 4 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 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, 14, 257)-net over F256, using
- 4 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- digital (0, 5, 129)-net over F128, using
(7, 17, 390)-Net over F128 — Digital
Digital (7, 17, 390)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12817, 390, F128, 10) (dual of [390, 373, 11]-code), using
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(12816, 383, F128, 10) (dual of [383, 367, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(12816, 382, F128, 10) (dual of [382, 366, 11]-code), using an extension Ce(9) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12815, 382, F128, 9) (dual of [382, 367, 10]-code), using an extension Ce(8) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1280, 1, F128, 0) (dual of [1, 1, 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(9) ⊂ Ce(8) [i] based on
- 6 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0) [i] based on linear OA(12816, 383, F128, 10) (dual of [383, 367, 11]-code), using
(7, 17, 299601)-Net in Base 128 — Upper bound on s
There is no (7, 17, 299602)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 664623 480810 292981 312414 077268 716068 > 12817 [i]