Best Known (101−46, 101, s)-Nets in Base 27
(101−46, 101, 222)-Net over F27 — Constructive and digital
Digital (55, 101, 222)-net over F27, using
- 1 times m-reduction [i] based on digital (55, 102, 222)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (4, 19, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- 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 (7, 54, 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 (4, 19, 64)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(101−46, 101, 370)-Net in Base 27 — Constructive
(55, 101, 370)-net in base 27, using
- t-expansion [i] based on (43, 101, 370)-net in base 27, using
- 7 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
- 7 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(101−46, 101, 1129)-Net over F27 — Digital
Digital (55, 101, 1129)-net over F27, using
(101−46, 101, 699889)-Net in Base 27 — Upper bound on s
There is no (55, 101, 699890)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 696130 714037 570659 901667 299081 342657 649918 126519 928552 262093 548421 679812 118248 780495 722565 837290 189081 914872 453576 453487 668924 050669 690269 885369 > 27101 [i]