Best Known (47, 105, s)-Nets in Base 27
(47, 105, 178)-Net over F27 — Constructive and digital
Digital (47, 105, 178)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (8, 37, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- digital (10, 68, 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 (8, 37, 84)-net over F27, using
(47, 105, 358)-Net over F27 — Digital
Digital (47, 105, 358)-net over F27, using
(47, 105, 370)-Net in Base 27 — Constructive
(47, 105, 370)-net in base 27, using
- t-expansion [i] based on (43, 105, 370)-net in base 27, using
- 3 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
- 3 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(47, 105, 68324)-Net in Base 27 — Upper bound on s
There is no (47, 105, 68325)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 964643 052286 919828 718238 339010 469273 935454 148949 606019 970146 846369 908853 135384 823190 847854 919763 522234 167592 273635 275413 558289 084021 946308 517683 187859 > 27105 [i]