Best Known (76−43, 76, s)-Nets in Base 27
(76−43, 76, 152)-Net over F27 — Constructive and digital
Digital (33, 76, 152)-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 (6, 49, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 27, 76)-net over F27, using
(76−43, 76, 224)-Net in Base 27 — Constructive
(33, 76, 224)-net in base 27, using
- 4 times m-reduction [i] based on (33, 80, 224)-net in base 27, using
- base change [i] based on digital (13, 60, 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, 60, 224)-net over F81, using
(76−43, 76, 242)-Net over F27 — Digital
Digital (33, 76, 242)-net over F27, using
(76−43, 76, 298)-Net in Base 27
(33, 76, 298)-net in base 27, using
- 8 times m-reduction [i] based on (33, 84, 298)-net in base 27, using
- base change [i] based on digital (12, 63, 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, 63, 298)-net over F81, using
(76−43, 76, 43194)-Net in Base 27 — Upper bound on s
There is no (33, 76, 43195)-net in base 27, because
- 1 times m-reduction [i] would yield (33, 75, 43195)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 225154 669918 782376 146126 947203 773553 208171 288574 582058 153419 920041 555363 150017 315012 769365 614635 805267 748407 > 2775 [i]