Best Known (35, 35+47, s)-Nets in Base 27
(35, 35+47, 152)-Net over F27 — Constructive and digital
Digital (35, 82, 152)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 29, 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, 53, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (6, 29, 76)-net over F27, using
(35, 35+47, 224)-Net in Base 27 — Constructive
(35, 82, 224)-net in base 27, using
- 6 times m-reduction [i] based on (35, 88, 224)-net in base 27, using
- base change [i] based on digital (13, 66, 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, 66, 224)-net over F81, using
(35, 35+47, 239)-Net over F27 — Digital
Digital (35, 82, 239)-net over F27, using
(35, 35+47, 298)-Net in Base 27
(35, 82, 298)-net in base 27, using
- 10 times m-reduction [i] based on (35, 92, 298)-net in base 27, using
- base change [i] based on digital (12, 69, 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, 69, 298)-net over F81, using
(35, 35+47, 39833)-Net in Base 27 — Upper bound on s
There is no (35, 82, 39834)-net in base 27, because
- 1 times m-reduction [i] would yield (35, 81, 39834)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 87 239316 043479 724810 535271 136933 182246 090154 915210 245639 202839 903543 892977 542237 457267 370949 680691 225664 798271 673049 > 2781 [i]