Best Known (8, 8+10, s)-Nets in Base 128
(8, 8+10, 387)-Net over F128 — Constructive and digital
Digital (8, 18, 387)-net over F128, using
- 1 times m-reduction [i] based on digital (8, 19, 387)-net over F128, using
- generalized (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 (0, 5, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 11, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 3, 129)-net over F128, using
- generalized (u, u+v)-construction [i] based on
(8, 8+10, 514)-Net in Base 128 — Constructive
(8, 18, 514)-net in base 128, using
- (u, u+v)-construction [i] based on
- (1, 6, 257)-net in base 128, using
- 2 times m-reduction [i] based on (1, 8, 257)-net in base 128, using
- base change [i] based on digital (0, 7, 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, 7, 257)-net over F256, using
- 2 times m-reduction [i] based on (1, 8, 257)-net in base 128, 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 (see above)
- 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
- (1, 6, 257)-net in base 128, using
(8, 8+10, 542)-Net over F128 — Digital
Digital (8, 18, 542)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12818, 542, F128, 10) (dual of [542, 524, 11]-code), using
- 157 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 150 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
- 157 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 150 times 0) [i] based on linear OA(12816, 383, F128, 10) (dual of [383, 367, 11]-code), using
(8, 8+10, 790655)-Net in Base 128 — Upper bound on s
There is no (8, 18, 790656)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 85 070858 316920 595314 228006 507325 841185 > 12818 [i]