Best Known (65−48, 65, s)-Nets in Base 8
(65−48, 65, 65)-Net over F8 — Constructive and digital
Digital (17, 65, 65)-net over F8, using
- t-expansion [i] based on digital (14, 65, 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
(65−48, 65, 376)-Net in Base 8 — Upper bound on s
There is no (17, 65, 377)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 52722 783178 001343 870367 368972 872059 446115 476806 565542 737087 > 865 [i]