Best Known (34, 56, s)-Nets in Base 27
(34, 56, 218)-Net over F27 — Constructive and digital
Digital (34, 56, 218)-net over F27, using
- 1 times m-reduction [i] based on digital (34, 57, 218)-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, 17, 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, 29, 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
- generalized (u, u+v)-construction [i] based on
(34, 56, 370)-Net in Base 27 — Constructive
(34, 56, 370)-net in base 27, using
- 16 times m-reduction [i] based on (34, 72, 370)-net in base 27, using
- base change [i] based on digital (16, 54, 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, 54, 370)-net over F81, using
(34, 56, 2201)-Net over F27 — Digital
Digital (34, 56, 2201)-net over F27, using
(34, 56, 3655804)-Net in Base 27 — Upper bound on s
There is no (34, 56, 3655805)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 143 341334 573046 779498 053189 319882 566728 935432 311367 598398 544424 785442 706960 468499 > 2756 [i]