Best Known (84−53, 84, s)-Nets in Base 27
(84−53, 84, 114)-Net over F27 — Constructive and digital
Digital (31, 84, 114)-net over F27, using
- t-expansion [i] based on digital (23, 84, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(84−53, 84, 172)-Net in Base 27 — Constructive
(31, 84, 172)-net in base 27, using
- 12 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
(84−53, 84, 208)-Net over F27 — Digital
Digital (31, 84, 208)-net over F27, using
- t-expansion [i] based on digital (24, 84, 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
(84−53, 84, 244)-Net in Base 27
(31, 84, 244)-net in base 27, using
- 4 times m-reduction [i] based on (31, 88, 244)-net in base 27, using
- base change [i] based on digital (9, 66, 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, 66, 244)-net over F81, using
(84−53, 84, 15041)-Net in Base 27 — Upper bound on s
There is no (31, 84, 15042)-net in base 27, because
- 1 times m-reduction [i] would yield (31, 83, 15042)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 63644 479112 854949 463412 949994 245666 322206 492810 710970 614764 786696 827708 038438 988584 523592 999019 740021 886406 501217 801669 > 2783 [i]