Best Known (56, 89, s)-Nets in Base 27
(56, 89, 286)-Net over F27 — Constructive and digital
Digital (56, 89, 286)-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, 15, 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 (7, 40, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 12, 64)-net over F27, using
(56, 89, 470)-Net in Base 27 — Constructive
(56, 89, 470)-net in base 27, using
- 271 times duplication [i] based on (55, 88, 470)-net in base 27, using
- base change [i] based on digital (33, 66, 470)-net over F81, using
- (u, u+v)-construction [i] based on
- digital (1, 17, 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, 49, 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, 17, 100)-net over F81, using
- (u, u+v)-construction [i] based on
- base change [i] based on digital (33, 66, 470)-net over F81, using
(56, 89, 4725)-Net over F27 — Digital
Digital (56, 89, 4725)-net over F27, using
(56, 89, large)-Net in Base 27 — Upper bound on s
There is no (56, 89, large)-net in base 27, because
- 31 times m-reduction [i] would yield (56, 58, large)-net in base 27, but