Best Known (57, 57+46, s)-Nets in Base 27
(57, 57+46, 234)-Net over F27 — Constructive and digital
Digital (57, 103, 234)-net over F27, using
- 1 times m-reduction [i] based on digital (57, 104, 234)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 21, 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 (6, 29, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- 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 (6, 21, 76)-net over F27, using
- generalized (u, u+v)-construction [i] based on
(57, 57+46, 370)-Net in Base 27 — Constructive
(57, 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
(57, 57+46, 1303)-Net over F27 — Digital
Digital (57, 103, 1303)-net over F27, using
(57, 57+46, 932175)-Net in Base 27 — Upper bound on s
There is no (57, 103, 932176)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2694 461743 576889 619201 154974 147767 120611 843270 774721 603784 163064 204179 765941 900037 295993 640717 196627 009633 380542 658441 573599 539279 008397 979721 641793 > 27103 [i]