Best Known (72−54, 72, s)-Nets in Base 8
(72−54, 72, 65)-Net over F8 — Constructive and digital
Digital (18, 72, 65)-net over F8, using
- t-expansion [i] based on digital (14, 72, 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
(72−54, 72, 382)-Net in Base 8 — Upper bound on s
There is no (18, 72, 383)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 106113 731510 453650 162855 702498 050872 440955 321729 299729 134718 137316 > 872 [i]