Best Known (59−41, 59, s)-Nets in Base 8
(59−41, 59, 65)-Net over F8 — Constructive and digital
Digital (18, 59, 65)-net over F8, using
- t-expansion [i] based on 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
(59−41, 59, 481)-Net in Base 8 — Upper bound on s
There is no (18, 59, 482)-net in base 8, because
- 1 times m-reduction [i] would yield (18, 58, 482)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 24829 926739 335378 767629 361825 980630 176636 158286 113912 > 858 [i]