Best Known (14, 14+19, s)-Nets in Base 128
(14, 14+19, 345)-Net over F128 — Constructive and digital
Digital (14, 33, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (5, 24, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (0, 9, 129)-net over F128, using
(14, 14+19, 445)-Net over F128 — Digital
Digital (14, 33, 445)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12833, 445, F128, 19) (dual of [445, 412, 20]-code), using
- 60 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 57 times 0) [i] based on linear OA(12831, 383, F128, 19) (dual of [383, 352, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(12831, 382, F128, 19) (dual of [382, 351, 20]-code), using an extension Ce(18) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12830, 382, F128, 18) (dual of [382, 352, 19]-code), using an extension Ce(17) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(18) ⊂ Ce(17) [i] based on
- 60 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 57 times 0) [i] based on linear OA(12831, 383, F128, 19) (dual of [383, 352, 20]-code), using
(14, 14+19, 514)-Net in Base 128 — Constructive
(14, 33, 514)-net in base 128, using
- 1281 times duplication [i] based on (13, 32, 514)-net in base 128, using
- base change [i] based on digital (9, 28, 514)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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
- digital (0, 19, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- digital (0, 9, 257)-net over F256, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (9, 28, 514)-net over F256, using
(14, 14+19, 1014490)-Net in Base 128 — Upper bound on s
There is no (14, 33, 1014491)-net in base 128, because
- 1 times m-reduction [i] would yield (14, 32, 1014491)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 26 960002 435628 840351 464235 273527 238844 935711 239245 179589 343567 434154 > 12832 [i]