Best Known (44, 44+25, s)-Nets in Base 81
(44, 44+25, 756)-Net over F81 — Constructive and digital
Digital (44, 69, 756)-net over F81, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 82)-net over F81, using
- digital (0, 3, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- digital (0, 3, 82)-net over F81 (see above)
- digital (0, 4, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 5, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 6, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 8, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (0, 12, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (1, 26, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
(44, 44+25, 37610)-Net over F81 — Digital
Digital (44, 69, 37610)-net over F81, using
(44, 44+25, large)-Net in Base 81 — Upper bound on s
There is no (44, 69, large)-net in base 81, because
- 23 times m-reduction [i] would yield (44, 46, large)-net in base 81, but