Best Known (18, 18+52, s)-Nets in Base 8
(18, 18+52, 65)-Net over F8 — Constructive and digital
Digital (18, 70, 65)-net over F8, using
- t-expansion [i] based on digital (14, 70, 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
(18, 18+52, 390)-Net in Base 8 — Upper bound on s
There is no (18, 70, 391)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 1647 722719 441393 035789 852695 503278 735672 124906 200036 263640 964144 > 870 [i]