Best Known (91−58, 91, s)-Nets in Base 27
(91−58, 91, 114)-Net over F27 — Constructive and digital
Digital (33, 91, 114)-net over F27, using
- t-expansion [i] based on digital (23, 91, 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
(91−58, 91, 172)-Net in Base 27 — Constructive
(33, 91, 172)-net in base 27, using
- 13 times m-reduction [i] based on (33, 104, 172)-net in base 27, using
- base change [i] based on digital (7, 78, 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, 78, 172)-net over F81, using
(91−58, 91, 220)-Net over F27 — Digital
Digital (33, 91, 220)-net over F27, using
- net from sequence [i] based on digital (33, 219)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 33 and N(F) ≥ 220, using
(91−58, 91, 244)-Net in Base 27
(33, 91, 244)-net in base 27, using
- 5 times m-reduction [i] based on (33, 96, 244)-net in base 27, using
- base change [i] based on digital (9, 72, 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, 72, 244)-net over F81, using
(91−58, 91, 13905)-Net in Base 27 — Upper bound on s
There is no (33, 91, 13906)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 17956 922308 666714 270498 202756 767220 406176 011630 790455 902726 050765 970022 898140 797191 836066 306829 524375 224860 539119 759666 364772 875773 > 2791 [i]