Best Known (41, 41+57, s)-Nets in Base 27
(41, 41+57, 158)-Net over F27 — Constructive and digital
Digital (41, 98, 158)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (6, 34, 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, 64, 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 (6, 34, 76)-net over F27, using
(41, 41+57, 273)-Net over F27 — Digital
Digital (41, 98, 273)-net over F27, using
- t-expansion [i] based on digital (40, 98, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
(41, 41+57, 370)-Net in Base 27 — Constructive
(41, 98, 370)-net in base 27, using
- 2 times m-reduction [i] based on (41, 100, 370)-net in base 27, using
- base change [i] based on digital (16, 75, 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, 75, 370)-net over F81, using
(41, 41+57, 39493)-Net in Base 27 — Upper bound on s
There is no (41, 98, 39494)-net in base 27, because
- 1 times m-reduction [i] would yield (41, 97, 39494)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 6 957791 058880 017954 280130 432449 969685 242028 362006 694722 045516 691370 412672 603391 613466 376018 751442 460773 187625 939934 125399 779706 251622 045433 > 2797 [i]