Best Known (125−36, 125, s)-Nets in Base 8
(125−36, 125, 514)-Net over F8 — Constructive and digital
Digital (89, 125, 514)-net over F8, using
- 1 times m-reduction [i] based on digital (89, 126, 514)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (20, 38, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 19, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 19, 80)-net over F64, using
- digital (51, 88, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 44, 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, 44, 177)-net over F64, using
- digital (20, 38, 160)-net over F8, using
- (u, u+v)-construction [i] based on
(125−36, 125, 590)-Net in Base 8 — Constructive
(89, 125, 590)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (1, 19, 14)-net over F8, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 1 and N(F) ≥ 14, using
- net from sequence [i] based on digital (1, 13)-sequence over F8, using
- (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
- digital (1, 19, 14)-net over F8, using
(125−36, 125, 3781)-Net over F8 — Digital
Digital (89, 125, 3781)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8125, 3781, F8, 36) (dual of [3781, 3656, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(8125, 4096, F8, 36) (dual of [4096, 3971, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(8125, 4096, F8, 36) (dual of [4096, 3971, 37]-code), using
(125−36, 125, 2015987)-Net in Base 8 — Upper bound on s
There is no (89, 125, 2015988)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 76957 260457 366771 052252 764871 755870 723399 596767 611425 727473 327963 366615 141807 829753 227288 503911 142829 680969 409721 > 8125 [i]