Best Known (28, 28+40, s)-Nets in Base 27
(28, 28+40, 128)-Net over F27 — Constructive and digital
Digital (28, 68, 128)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 24, 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 (4, 44, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27 (see above)
- digital (4, 24, 64)-net over F27, using
(28, 28+40, 172)-Net in Base 27 — Constructive
(28, 68, 172)-net in base 27, using
- 16 times m-reduction [i] based on (28, 84, 172)-net in base 27, using
- base change [i] based on digital (7, 63, 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, 63, 172)-net over F81, using
(28, 28+40, 208)-Net over F27 — Digital
Digital (28, 68, 208)-net over F27, using
- t-expansion [i] based on digital (24, 68, 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
(28, 28+40, 244)-Net in Base 27
(28, 68, 244)-net in base 27, using
- 8 times m-reduction [i] based on (28, 76, 244)-net in base 27, using
- base change [i] based on digital (9, 57, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- base change [i] based on digital (9, 57, 244)-net over F81, using
(28, 28+40, 23484)-Net in Base 27 — Upper bound on s
There is no (28, 68, 23485)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 21 525362 817699 701893 665053 361940 873466 732135 611220 021836 513299 512458 435839 141267 723129 042475 661553 > 2768 [i]