Best Known (65−42, 65, s)-Nets in Base 27
(65−42, 65, 114)-Net over F27 — Constructive and digital
Digital (23, 65, 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
(65−42, 65, 160)-Net in Base 27 — Constructive
(23, 65, 160)-net in base 27, using
- 7 times m-reduction [i] based on (23, 72, 160)-net in base 27, using
- base change [i] based on digital (5, 54, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 54, 160)-net over F81, using
(65−42, 65, 163)-Net over F27 — Digital
Digital (23, 65, 163)-net over F27, using
- t-expansion [i] based on digital (21, 65, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
(65−42, 65, 190)-Net in Base 27
(23, 65, 190)-net in base 27, using
- 3 times m-reduction [i] based on (23, 68, 190)-net in base 27, using
- base change [i] based on digital (6, 51, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 51, 190)-net over F81, using
(65−42, 65, 8982)-Net in Base 27 — Upper bound on s
There is no (23, 65, 8983)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1093 726975 873692 384721 626705 711340 536023 747993 915325 476294 145364 129295 018313 717509 754725 325327 > 2765 [i]