Best Known (31, 31+39, s)-Nets in Base 8
(31, 31+39, 69)-Net over F8 — Constructive and digital
Digital (31, 70, 69)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 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, 48, 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, 22, 24)-net over F8, using
(31, 31+39, 97)-Net over F8 — Digital
Digital (31, 70, 97)-net over F8, using
- t-expansion [i] based on digital (28, 70, 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
(31, 31+39, 2144)-Net in Base 8 — Upper bound on s
There is no (31, 70, 2145)-net in base 8, because
- 1 times m-reduction [i] would yield (31, 69, 2145)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 205 945284 859282 515835 394391 560417 374774 207722 402485 470530 480800 > 869 [i]