Best Known (77−32, 77, s)-Nets in Base 27
(77−32, 77, 234)-Net over F27 — Constructive and digital
Digital (45, 77, 234)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 16, 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, 22, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (7, 39, 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, 16, 76)-net over F27, using
(77−32, 77, 370)-Net in Base 27 — Constructive
(45, 77, 370)-net in base 27, using
- t-expansion [i] based on (43, 77, 370)-net in base 27, using
- 31 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
- 31 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(77−32, 77, 1731)-Net over F27 — Digital
Digital (45, 77, 1731)-net over F27, using
(77−32, 77, 2023027)-Net in Base 27 — Upper bound on s
There is no (45, 77, 2023028)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 164 063566 433598 806429 029153 443188 195173 710679 664535 029974 451143 325367 985411 473792 374795 489468 427165 694066 500737 > 2777 [i]