Best Known (104, 104+56, s)-Nets in Base 8
(104, 104+56, 382)-Net over F8 — Constructive and digital
Digital (104, 160, 382)-net over F8, using
- 1 times m-reduction [i] based on digital (104, 161, 382)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (5, 33, 28)-net over F8, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 5 and N(F) ≥ 28, using
- net from sequence [i] based on digital (5, 27)-sequence over F8, using
- digital (71, 128, 354)-net over F8, using
- trace code for nets [i] based on digital (7, 64, 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, 64, 177)-net over F64, using
- digital (5, 33, 28)-net over F8, using
- (u, u+v)-construction [i] based on
(104, 104+56, 576)-Net in Base 8 — Constructive
(104, 160, 576)-net in base 8, using
- 6 times m-reduction [i] based on (104, 166, 576)-net in base 8, using
- trace code for nets [i] based on (21, 83, 288)-net in base 64, using
- 1 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
- 1 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- trace code for nets [i] based on (21, 83, 288)-net in base 64, using
(104, 104+56, 1319)-Net over F8 — Digital
Digital (104, 160, 1319)-net over F8, using
(104, 104+56, 233554)-Net in Base 8 — Upper bound on s
There is no (104, 160, 233555)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 3 121850 728311 386173 739173 196405 704029 439493 778671 473706 690954 323537 163666 889819 091484 115504 643654 975509 176053 891478 036902 312528 573008 142178 682192 > 8160 [i]