Best Known (76−42, 76, s)-Nets in Base 27
(76−42, 76, 158)-Net over F27 — Constructive and digital
Digital (34, 76, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 27, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (7, 49, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (6, 27, 76)-net over F27, using
(76−42, 76, 224)-Net in Base 27 — Constructive
(34, 76, 224)-net in base 27, using
- 8 times m-reduction [i] based on (34, 84, 224)-net in base 27, using
- base change [i] based on digital (13, 63, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 63, 224)-net over F81, using
(76−42, 76, 277)-Net over F27 — Digital
Digital (34, 76, 277)-net over F27, using
(76−42, 76, 298)-Net in Base 27
(34, 76, 298)-net in base 27, using
- 12 times m-reduction [i] based on (34, 88, 298)-net in base 27, using
- base change [i] based on digital (12, 66, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 66, 298)-net over F81, using
(76−42, 76, 50535)-Net in Base 27 — Upper bound on s
There is no (34, 76, 50536)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 6 076656 502145 908161 631655 990786 181046 571917 613537 546263 474049 552505 387850 978925 079984 621531 553499 869548 580113 > 2776 [i]