Best Known (92−54, 92, s)-Nets in Base 27
(92−54, 92, 146)-Net over F27 — Constructive and digital
Digital (38, 92, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 31, 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 (7, 61, 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, 31, 64)-net over F27, using
(92−54, 92, 224)-Net in Base 27 — Constructive
(38, 92, 224)-net in base 27, using
- 8 times m-reduction [i] based on (38, 100, 224)-net in base 27, using
- base change [i] based on digital (13, 75, 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, 75, 224)-net over F81, using
(92−54, 92, 244)-Net over F27 — Digital
Digital (38, 92, 244)-net over F27, using
- t-expansion [i] based on digital (36, 92, 244)-net over F27, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 36 and N(F) ≥ 244, using
- net from sequence [i] based on digital (36, 243)-sequence over F27, using
(92−54, 92, 298)-Net in Base 27
(38, 92, 298)-net in base 27, using
- 12 times m-reduction [i] based on (38, 104, 298)-net in base 27, using
- base change [i] based on digital (12, 78, 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, 78, 298)-net over F81, using
(92−54, 92, 31657)-Net in Base 27 — Upper bound on s
There is no (38, 92, 31658)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 484785 388395 612168 865046 746391 199833 309353 468733 434308 065463 328924 743313 760510 075778 022415 840909 605547 096267 213994 255983 036441 385649 > 2792 [i]