Best Known (115−32, 115, s)-Nets in Base 8
(115−32, 115, 514)-Net over F8 — Constructive and digital
Digital (83, 115, 514)-net over F8, using
- 81 times duplication [i] based on digital (82, 114, 514)-net over F8, using
- t-expansion [i] based on digital (81, 114, 514)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (18, 34, 160)-net over F8, using
- trace code for nets [i] based on digital (1, 17, 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, 17, 80)-net over F64, using
- digital (47, 80, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 40, 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, 40, 177)-net over F64, using
- digital (18, 34, 160)-net over F8, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (81, 114, 514)-net over F8, using
(115−32, 115, 600)-Net in Base 8 — Constructive
(83, 115, 600)-net in base 8, using
- (u, u+v)-construction [i] based on
- digital (3, 19, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- (64, 96, 576)-net in base 8, using
- trace code for nets [i] based on (16, 48, 288)-net in base 64, using
- 1 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- base change [i] based on digital (9, 42, 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, 42, 288)-net over F128, using
- 1 times m-reduction [i] based on (16, 49, 288)-net in base 64, using
- trace code for nets [i] based on (16, 48, 288)-net in base 64, using
- digital (3, 19, 24)-net over F8, using
(115−32, 115, 4153)-Net over F8 — Digital
Digital (83, 115, 4153)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8115, 4153, F8, 32) (dual of [4153, 4038, 33]-code), using
- 54 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 46 times 0) [i] based on linear OA(8112, 4096, F8, 32) (dual of [4096, 3984, 33]-code), using
- 1 times truncation [i] based on linear OA(8113, 4097, F8, 33) (dual of [4097, 3984, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 88−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(8113, 4097, F8, 33) (dual of [4097, 3984, 34]-code), using
- 54 step Varšamov–Edel lengthening with (ri) = (2, 6 times 0, 1, 46 times 0) [i] based on linear OA(8112, 4096, F8, 32) (dual of [4096, 3984, 33]-code), using
(115−32, 115, 3008836)-Net in Base 8 — Upper bound on s
There is no (83, 115, 3008837)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 71 672115 274088 034177 386792 578184 306466 902470 428855 339637 219291 227811 811910 931254 525258 643860 830035 330140 > 8115 [i]