Best Known (133−75, 133, s)-Nets in Base 8
(133−75, 133, 99)-Net over F8 — Constructive and digital
Digital (58, 133, 99)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 44, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- digital (14, 89, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (7, 44, 34)-net over F8, using
(133−75, 133, 144)-Net over F8 — Digital
Digital (58, 133, 144)-net over F8, using
- t-expansion [i] based on digital (45, 133, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(133−75, 133, 3465)-Net in Base 8 — Upper bound on s
There is no (58, 133, 3466)-net in base 8, because
- 1 times m-reduction [i] would yield (58, 132, 3466)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 162526 497042 982677 598127 347310 355104 226348 363997 179572 572160 882599 052848 437774 202691 534188 704581 746603 086579 117322 455912 > 8132 [i]