Best Known (46, 46+54, s)-Nets in Base 27
(46, 46+54, 182)-Net over F27 — Constructive and digital
Digital (46, 100, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 36, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 64, 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 (9, 36, 88)-net over F27, using
(46, 46+54, 370)-Net in Base 27 — Constructive
(46, 100, 370)-net in base 27, using
- t-expansion [i] based on (43, 100, 370)-net in base 27, using
- 8 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
- 8 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(46, 46+54, 392)-Net over F27 — Digital
Digital (46, 100, 392)-net over F27, using
(46, 46+54, 84082)-Net in Base 27 — Upper bound on s
There is no (46, 100, 84083)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 136891 501350 776672 533239 623085 513832 929136 576587 893081 651408 784627 102669 906267 506893 868815 000161 569926 052146 314286 602325 938092 642393 860662 694995 > 27100 [i]