Best Known (99−28, 99, s)-Nets in Base 8
(99−28, 99, 484)-Net over F8 — Constructive and digital
Digital (71, 99, 484)-net over F8, using
- 1 times m-reduction [i] based on digital (71, 100, 484)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 28, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 14, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 14, 65)-net over F64, using
- digital (43, 72, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 36, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 36, 177)-net over F64, using
- digital (14, 28, 130)-net over F8, using
- (u, u+v)-construction [i] based on
(99−28, 99, 576)-Net in Base 8 — Constructive
(71, 99, 576)-net in base 8, using
- 9 times m-reduction [i] based on (71, 108, 576)-net in base 8, using
- trace code for nets [i] based on (17, 54, 288)-net in base 64, using
- 2 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 48, 288)-net over F128, using
- 2 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- trace code for nets [i] based on (17, 54, 288)-net in base 64, using
(99−28, 99, 3805)-Net over F8 — Digital
Digital (71, 99, 3805)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(899, 3805, F8, 28) (dual of [3805, 3706, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(899, 4107, F8, 28) (dual of [4107, 4008, 29]-code), using
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- linear OA(897, 4096, F8, 28) (dual of [4096, 3999, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(889, 4096, F8, 26) (dual of [4096, 4007, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(885, 4096, F8, 25) (dual of [4096, 4011, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(81, 10, F8, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(27) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(899, 4107, F8, 28) (dual of [4107, 4008, 29]-code), using
(99−28, 99, 2101330)-Net in Base 8 — Upper bound on s
There is no (71, 99, 2101331)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 254631 042277 969948 177354 492162 559837 665381 574856 747593 634495 227891 131906 865679 841935 583076 > 899 [i]