Best Known (41, 109, s)-Nets in Base 27
(41, 109, 116)-Net over F27 — Constructive and digital
Digital (41, 109, 116)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (3, 37, 52)-net over F27, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 3 and N(F) ≥ 52, using
- net from sequence [i] based on digital (3, 51)-sequence over F27, using
- digital (4, 72, 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 (3, 37, 52)-net over F27, using
(41, 109, 224)-Net in Base 27 — Constructive
(41, 109, 224)-net in base 27, using
- 271 times duplication [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
(41, 109, 273)-Net over F27 — Digital
Digital (41, 109, 273)-net over F27, using
- t-expansion [i] based on digital (40, 109, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
(41, 109, 298)-Net in Base 27
(41, 109, 298)-net in base 27, using
- 271 times duplication [i] based on (40, 108, 298)-net in base 27, using
- t-expansion [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- t-expansion [i] based on (39, 108, 298)-net in base 27, using
(41, 109, 20179)-Net in Base 27 — Upper bound on s
There is no (41, 109, 20180)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 045371 347032 853219 352594 622330 515349 175313 392623 245913 385811 611720 769155 727308 467438 119542 062889 221061 800179 491121 722242 684629 226054 382365 102625 149166 413593 > 27109 [i]