Best Known (64, 64+24, s)-Nets in Base 8
(64, 64+24, 514)-Net over F8 — Constructive and digital
Digital (64, 88, 514)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 26, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 13, 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, 13, 80)-net over F64, using
- digital (38, 62, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 31, 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, 31, 177)-net over F64, using
- digital (14, 26, 160)-net over F8, using
(64, 64+24, 644)-Net in Base 8 — Constructive
(64, 88, 644)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (12, 24, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 65)-net over F64, using
- (40, 64, 514)-net in base 8, using
- base change [i] based on digital (24, 48, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 24, 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
- trace code for nets [i] based on digital (0, 24, 257)-net over F256, using
- base change [i] based on digital (24, 48, 514)-net over F16, using
- digital (12, 24, 130)-net over F8, using
(64, 64+24, 4201)-Net over F8 — Digital
Digital (64, 88, 4201)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(888, 4201, F8, 24) (dual of [4201, 4113, 25]-code), using
- 102 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 24 times 0, 1, 70 times 0) [i] based on linear OA(884, 4095, F8, 24) (dual of [4095, 4011, 25]-code), using
- 1 times truncation [i] based on 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]
- 1 times truncation [i] based on linear OA(885, 4096, F8, 25) (dual of [4096, 4011, 26]-code), using
- 102 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 24 times 0, 1, 70 times 0) [i] based on linear OA(884, 4095, F8, 24) (dual of [4095, 4011, 25]-code), using
(64, 64+24, 3169000)-Net in Base 8 — Upper bound on s
There is no (64, 88, 3169001)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 29 642845 812393 080860 236228 287091 096265 742793 966317 248087 376102 456507 604871 571736 > 888 [i]