Best Known (47, 47+56, s)-Nets in Base 27
(47, 47+56, 182)-Net over F27 — Constructive and digital
Digital (47, 103, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 37, 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, 66, 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, 37, 88)-net over F27, using
(47, 47+56, 370)-Net in Base 27 — Constructive
(47, 103, 370)-net in base 27, using
- t-expansion [i] based on (43, 103, 370)-net in base 27, using
- 5 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
- 5 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(47, 47+56, 386)-Net over F27 — Digital
Digital (47, 103, 386)-net over F27, using
(47, 47+56, 80043)-Net in Base 27 — Upper bound on s
There is no (47, 103, 80044)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2694 840589 255275 973971 959874 184322 408487 632182 954607 584853 792166 113211 739399 781438 761015 208786 580018 798762 574575 875342 394035 897226 402596 719450 676289 > 27103 [i]