Best Known (85−48, 85, s)-Nets in Base 27
(85−48, 85, 158)-Net over F27 — Constructive and digital
Digital (37, 85, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 30, 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 (7, 55, 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 (6, 30, 76)-net over F27, using
(85−48, 85, 224)-Net in Base 27 — Constructive
(37, 85, 224)-net in base 27, using
- 11 times m-reduction [i] based on (37, 96, 224)-net in base 27, using
- base change [i] based on digital (13, 72, 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, 72, 224)-net over F81, using
(85−48, 85, 267)-Net over F27 — Digital
Digital (37, 85, 267)-net over F27, using
(85−48, 85, 298)-Net in Base 27
(37, 85, 298)-net in base 27, using
- 15 times m-reduction [i] based on (37, 100, 298)-net in base 27, using
- base change [i] based on digital (12, 75, 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, 75, 298)-net over F81, using
(85−48, 85, 44226)-Net in Base 27 — Upper bound on s
There is no (37, 85, 44227)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 46 353380 088412 933334 356552 195406 577844 311847 261263 877262 521963 960877 641649 810778 733018 149388 902027 485369 104294 407528 862353 > 2785 [i]