Best Known (58−32, 58, s)-Nets in Base 8
(58−32, 58, 65)-Net over F8 — Constructive and digital
Digital (26, 58, 65)-net over F8, using
- t-expansion [i] based on digital (14, 58, 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
(58−32, 58, 86)-Net over F8 — Digital
Digital (26, 58, 86)-net over F8, using
- t-expansion [i] based on digital (25, 58, 86)-net over F8, using
- net from sequence [i] based on digital (25, 85)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 25 and N(F) ≥ 86, using
- net from sequence [i] based on digital (25, 85)-sequence over F8, using
(58−32, 58, 1814)-Net in Base 8 — Upper bound on s
There is no (26, 58, 1815)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 24003 583366 105283 785187 315977 962515 092506 240430 368901 > 858 [i]