Best Known (34, 34+26, s)-Nets in Base 27
(34, 34+26, 196)-Net over F27 — Constructive and digital
Digital (34, 60, 196)-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, 17, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (5, 31, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 12, 64)-net over F27, using
(34, 34+26, 370)-Net in Base 27 — Constructive
(34, 60, 370)-net in base 27, using
- 12 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, 34+26, 1079)-Net over F27 — Digital
Digital (34, 60, 1079)-net over F27, using
(34, 34+26, 880488)-Net in Base 27 — Upper bound on s
There is no (34, 60, 880489)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 76 177380 876244 388794 532719 728819 926746 014688 858480 339519 570325 182477 051382 525481 555099 > 2760 [i]