Best Known (104−58, 104, s)-Nets in Base 27
(104−58, 104, 176)-Net over F27 — Constructive and digital
Digital (46, 104, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 36, 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 (10, 68, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (7, 36, 82)-net over F27, using
(104−58, 104, 337)-Net over F27 — Digital
Digital (46, 104, 337)-net over F27, using
(104−58, 104, 370)-Net in Base 27 — Constructive
(46, 104, 370)-net in base 27, using
- t-expansion [i] based on (43, 104, 370)-net in base 27, using
- 4 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 81, 370)-net over F81, using
- 4 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(104−58, 104, 60982)-Net in Base 27 — Upper bound on s
There is no (46, 104, 60983)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 72755 226045 224504 389652 165341 115580 404388 299417 623180 786870 349850 212437 122509 638261 411509 501722 857780 257245 908285 572652 798193 089774 234985 731891 546239 > 27104 [i]