Best Known (107−65, 107, s)-Nets in Base 27
(107−65, 107, 140)-Net over F27 — Constructive and digital
Digital (42, 107, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 36, 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 (6, 71, 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 (4, 36, 64)-net over F27, using
(107−65, 107, 224)-Net in Base 27 — Constructive
(42, 107, 224)-net in base 27, using
- t-expansion [i] based on (40, 107, 224)-net in base 27, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
(107−65, 107, 280)-Net over F27 — Digital
Digital (42, 107, 280)-net over F27, using
- net from sequence [i] based on digital (42, 279)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 42 and N(F) ≥ 280, using
(107−65, 107, 298)-Net in Base 27
(42, 107, 298)-net in base 27, using
- t-expansion [i] based on (39, 107, 298)-net in base 27, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(107−65, 107, 27103)-Net in Base 27 — Upper bound on s
There is no (42, 107, 27104)-net in base 27, because
- 1 times m-reduction [i] would yield (42, 106, 27104)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 53 041843 082762 151158 655454 394706 824546 202671 802149 694300 390514 875084 749114 474908 320753 520481 495094 091101 282249 592874 673627 060738 202534 266642 459367 780353 > 27106 [i]