Best Known (45−16, 45, s)-Nets in Base 8
(45−16, 45, 256)-Net over F8 — Constructive and digital
Digital (29, 45, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (29, 48, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 24, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 24, 128)-net over F64, using
(45−16, 45, 514)-Net in Base 8 — Constructive
(29, 45, 514)-net in base 8, using
- 1 times m-reduction [i] based on (29, 46, 514)-net in base 8, using
- trace code for nets [i] based on (6, 23, 257)-net in base 64, using
- 1 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- base change [i] based on digital (0, 18, 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
- base change [i] based on digital (0, 18, 257)-net over F256, using
- 1 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
- trace code for nets [i] based on (6, 23, 257)-net in base 64, using
(45−16, 45, 535)-Net over F8 — Digital
Digital (29, 45, 535)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(845, 535, F8, 16) (dual of [535, 490, 17]-code), using
- 20 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0) [i] based on linear OA(842, 512, F8, 16) (dual of [512, 470, 17]-code), using
- 1 times truncation [i] based on linear OA(843, 513, F8, 17) (dual of [513, 470, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513 | 86−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(843, 513, F8, 17) (dual of [513, 470, 18]-code), using
- 20 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0) [i] based on linear OA(842, 512, F8, 16) (dual of [512, 470, 17]-code), using
(45−16, 45, 64631)-Net in Base 8 — Upper bound on s
There is no (29, 45, 64632)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 43560 627176 069278 659992 288836 592390 475670 > 845 [i]