Best Known (63, 63+24, s)-Nets in Base 8
(63, 63+24, 484)-Net over F8 — Constructive and digital
Digital (63, 87, 484)-net over F8, using
- 1 times m-reduction [i] based on digital (63, 88, 484)-net over F8, 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
- digital (39, 64, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 32, 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, 32, 177)-net over F64, using
- digital (12, 24, 130)-net over F8, using
- (u, u+v)-construction [i] based on
(63, 63+24, 579)-Net in Base 8 — Constructive
(63, 87, 579)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (11, 23, 65)-net over F8, using
- base reduction for projective spaces (embedding PG(11,64) in PG(22,8)) 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
- base reduction for projective spaces (embedding PG(11,64) in PG(22,8)) 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 (11, 23, 65)-net over F8, using
(63, 63+24, 4129)-Net over F8 — Digital
Digital (63, 87, 4129)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(887, 4129, F8, 24) (dual of [4129, 4042, 25]-code), using
- 31 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 24 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
- 31 step Varšamov–Edel lengthening with (ri) = (2, 5 times 0, 1, 24 times 0) [i] based on linear OA(884, 4095, F8, 24) (dual of [4095, 4011, 25]-code), using
(63, 63+24, 2664799)-Net in Base 8 — Upper bound on s
There is no (63, 87, 2664800)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 705348 501323 589732 884603 534915 429516 981438 017818 224560 017021 077751 536541 891461 > 887 [i]