Best Known (81−45, 81, s)-Nets in Base 8
(81−45, 81, 74)-Net over F8 — Constructive and digital
Digital (36, 81, 74)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (0, 22, 9)-net over F8, using
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 0 and N(F) ≥ 9, using
- the rational function field F8(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 8)-sequence over F8, using
- digital (14, 59, 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 (0, 22, 9)-net over F8, using
(81−45, 81, 112)-Net over F8 — Digital
Digital (36, 81, 112)-net over F8, using
- t-expansion [i] based on digital (35, 81, 112)-net over F8, using
- net from sequence [i] based on digital (35, 111)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 35 and N(F) ≥ 112, using
- net from sequence [i] based on digital (35, 111)-sequence over F8, using
(81−45, 81, 2473)-Net in Base 8 — Upper bound on s
There is no (36, 81, 2474)-net in base 8, because
- 1 times m-reduction [i] would yield (36, 80, 2474)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1 772710 638569 717235 798868 314891 693758 956678 766865 044049 384464 740050 072792 > 880 [i]