Best Known (85−54, 85, s)-Nets in Base 27
(85−54, 85, 114)-Net over F27 — Constructive and digital
Digital (31, 85, 114)-net over F27, using
- t-expansion [i] based on digital (23, 85, 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
(85−54, 85, 172)-Net in Base 27 — Constructive
(31, 85, 172)-net in base 27, using
- 11 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
(85−54, 85, 208)-Net over F27 — Digital
Digital (31, 85, 208)-net over F27, using
- t-expansion [i] based on digital (24, 85, 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
(85−54, 85, 244)-Net in Base 27
(31, 85, 244)-net in base 27, using
- 3 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
(85−54, 85, 13462)-Net in Base 27 — Upper bound on s
There is no (31, 85, 13463)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 46 381562 137066 050684 952736 847068 102838 687408 155550 869170 111528 972968 106440 433982 067536 244319 852274 547213 867364 256501 329635 > 2785 [i]