Best Known (54, 54+31, s)-Nets in Base 27
(54, 54+31, 294)-Net over F27 — Constructive and digital
Digital (54, 85, 294)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 11, 66)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- digital (1, 8, 38)-net over F27, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 1 and N(F) ≥ 38, using
- net from sequence [i] based on digital (1, 37)-sequence over F27, using
- digital (0, 3, 28)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 16, 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, 21, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 37, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (4, 11, 66)-net over F27, using
(54, 54+31, 470)-Net in Base 27 — Constructive
(54, 85, 470)-net in base 27, using
- 271 times duplication [i] based on (53, 84, 470)-net in base 27, using
- base change [i] based on digital (32, 63, 470)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 16, 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 (16, 47, 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
- digital (1, 16, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (32, 63, 470)-net over F81, using
(54, 54+31, 5279)-Net over F27 — Digital
Digital (54, 85, 5279)-net over F27, using
(54, 54+31, large)-Net in Base 27 — Upper bound on s
There is no (54, 85, large)-net in base 27, because
- 29 times m-reduction [i] would yield (54, 56, large)-net in base 27, but