Best Known (66−36, 66, s)-Nets in Base 8
(66−36, 66, 69)-Net over F8 — Constructive and digital
Digital (30, 66, 69)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 21, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- digital (9, 45, 45)-net over F8, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using
- net from sequence [i] based on digital (9, 44)-sequence over F8, using
- digital (3, 21, 24)-net over F8, using
(66−36, 66, 97)-Net over F8 — Digital
Digital (30, 66, 97)-net over F8, using
- t-expansion [i] based on digital (28, 66, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
(66−36, 66, 2198)-Net in Base 8 — Upper bound on s
There is no (30, 66, 2199)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 402416 599414 824364 287533 761049 671295 324205 148008 626714 398475 > 866 [i]