Best Known (91−54, 91, s)-Nets in Base 27
(91−54, 91, 140)-Net over F27 — Constructive and digital
Digital (37, 91, 140)-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 (6, 60, 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, 31, 64)-net over F27, using
(91−54, 91, 224)-Net in Base 27 — Constructive
(37, 91, 224)-net in base 27, using
- 5 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
(91−54, 91, 244)-Net over F27 — Digital
Digital (37, 91, 244)-net over F27, using
- t-expansion [i] based on digital (36, 91, 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
(91−54, 91, 298)-Net in Base 27
(37, 91, 298)-net in base 27, using
- 9 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
(91−54, 91, 28018)-Net in Base 27 — Upper bound on s
There is no (37, 91, 28019)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 17963 526965 154860 539085 900965 673788 323370 057284 705296 888847 394083 948448 844815 948134 181640 081031 029958 931073 336810 242144 818957 639763 > 2791 [i]