Best Known (31, 47, s)-Nets in Base 8
(31, 47, 354)-Net over F8 — Constructive and digital
Digital (31, 47, 354)-net over F8, using
- 1 times m-reduction [i] based on digital (31, 48, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 24, 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, 24, 177)-net over F64, using
(31, 47, 516)-Net in Base 8 — Constructive
(31, 47, 516)-net in base 8, using
- 1 times m-reduction [i] based on (31, 48, 516)-net in base 8, using
- base change [i] based on digital (19, 36, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 18, 258)-net over F256, using
- base change [i] based on digital (19, 36, 516)-net over F16, using
(31, 47, 635)-Net over F8 — Digital
Digital (31, 47, 635)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(847, 635, F8, 16) (dual of [635, 588, 17]-code), using
- 118 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0, 1, 34 times 0, 1, 62 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
- 118 step Varšamov–Edel lengthening with (ri) = (2, 4 times 0, 1, 14 times 0, 1, 34 times 0, 1, 62 times 0) [i] based on linear OA(842, 512, F8, 16) (dual of [512, 470, 17]-code), using
(31, 47, 108699)-Net in Base 8 — Upper bound on s
There is no (31, 47, 108700)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 2 787716 096724 949287 315201 510073 002583 799131 > 847 [i]