Best Known (98−28, 98, s)-Nets in Base 8
(98−28, 98, 484)-Net over F8 — Constructive and digital
Digital (70, 98, 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 (42, 70, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 35, 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, 35, 177)-net over F64, using
- digital (14, 28, 130)-net over F8, using
(98−28, 98, 576)-Net in Base 8 — Constructive
(70, 98, 576)-net in base 8, using
- 8 times m-reduction [i] based on (70, 106, 576)-net in base 8, using
- trace code for nets [i] based on (17, 53, 288)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (17, 56, 288)-net in base 64, using
- trace code for nets [i] based on (17, 53, 288)-net in base 64, using
(98−28, 98, 3512)-Net over F8 — Digital
Digital (70, 98, 3512)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(898, 3512, F8, 28) (dual of [3512, 3414, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(898, 4105, F8, 28) (dual of [4105, 4007, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(898, 4105, F8, 28) (dual of [4105, 4007, 29]-code), using
(98−28, 98, 1811288)-Net in Base 8 — Upper bound on s
There is no (70, 98, 1811289)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 31828 871129 101419 770590 517451 495988 961199 166893 053879 662357 393849 191980 818880 135680 384136 > 898 [i]