Best Known (6, 6+10, s)-Nets in Base 81
(6, 6+10, 182)-Net over F81 — Constructive and digital
Digital (6, 16, 182)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (1, 11, 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
- digital (0, 5, 82)-net over F81, using
(6, 6+10, 190)-Net over F81 — Digital
Digital (6, 16, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
(6, 6+10, 41675)-Net in Base 81 — Upper bound on s
There is no (6, 16, 41676)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 3 434047 479355 138082 696068 254401 > 8116 [i]