Best Known (31, 31+45, s)-Nets in Base 27
(31, 31+45, 132)-Net over F27 — Constructive and digital
Digital (31, 76, 132)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 26, 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 (5, 50, 68)-net over F27, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 5 and N(F) ≥ 68, using
- net from sequence [i] based on digital (5, 67)-sequence over F27, using
- digital (4, 26, 64)-net over F27, using
(31, 31+45, 172)-Net in Base 27 — Constructive
(31, 76, 172)-net in base 27, using
- 20 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
(31, 31+45, 208)-Net over F27 — Digital
Digital (31, 76, 208)-net over F27, using
- t-expansion [i] based on digital (24, 76, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
(31, 31+45, 298)-Net in Base 27
(31, 76, 298)-net in base 27, using
- base change [i] based on digital (12, 57, 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
(31, 31+45, 26384)-Net in Base 27 — Upper bound on s
There is no (31, 76, 26385)-net in base 27, because
- 1 times m-reduction [i] would yield (31, 75, 26385)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 225221 885044 074747 293244 421865 724643 029032 791938 309318 746007 952956 806037 984940 157655 229772 000736 781749 196713 > 2775 [i]