Best Known (54, 86, s)-Nets in Base 27
(54, 86, 280)-Net over F27 — Constructive and digital
Digital (54, 86, 280)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 12, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (4, 14, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (6, 22, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (6, 38, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (4, 12, 64)-net over F27, using
(54, 86, 452)-Net in Base 27 — Constructive
(54, 86, 452)-net in base 27, using
- (u, u+v)-construction [i] based on
- (6, 22, 82)-net in base 27, using
- 2 times m-reduction [i] based on (6, 24, 82)-net in base 27, using
- base change [i] based on digital (0, 18, 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
- base change [i] based on digital (0, 18, 82)-net over F81, using
- 2 times m-reduction [i] based on (6, 24, 82)-net in base 27, using
- (32, 64, 370)-net in base 27, using
- base change [i] based on digital (16, 48, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 48, 370)-net over F81, using
- (6, 22, 82)-net in base 27, using
(54, 86, 4482)-Net over F27 — Digital
Digital (54, 86, 4482)-net over F27, using
(54, 86, large)-Net in Base 27 — Upper bound on s
There is no (54, 86, large)-net in base 27, because
- 30 times m-reduction [i] would yield (54, 56, large)-net in base 27, but