Best Known (49, 49+26, s)-Nets in Base 81
(49, 49+26, 920)-Net over F81 — Constructive and digital
Digital (49, 75, 920)-net over F81, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 82)-net over F81, using
- digital (0, 2, 82)-net over F81 (see above)
- digital (0, 2, 82)-net over F81 (see above)
- 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, 13, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81 (see above)
- digital (1, 27, 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
(49, 49+26, 67619)-Net over F81 — Digital
Digital (49, 75, 67619)-net over F81, using
(49, 49+26, large)-Net in Base 81 — Upper bound on s
There is no (49, 75, large)-net in base 81, because
- 24 times m-reduction [i] would yield (49, 51, large)-net in base 81, but