Best Known (71−29, 71, s)-Nets in Base 27
(71−29, 71, 234)-Net over F27 — Constructive and digital
Digital (42, 71, 234)-net over F27, using
- generalized (u, u+v)-construction [i] based on
- digital (6, 15, 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, 20, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27 (see above)
- digital (7, 36, 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, 15, 76)-net over F27, using
(71−29, 71, 370)-Net in Base 27 — Constructive
(42, 71, 370)-net in base 27, using
- 33 times m-reduction [i] based on (42, 104, 370)-net in base 27, using
- base change [i] based on digital (16, 78, 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, 78, 370)-net over F81, using
(71−29, 71, 1866)-Net over F27 — Digital
Digital (42, 71, 1866)-net over F27, using
(71−29, 71, 3336585)-Net in Base 27 — Upper bound on s
There is no (42, 71, 3336586)-net in base 27, because
- 1 times m-reduction [i] would yield (42, 70, 3336586)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 15684 254121 947064 738571 214499 216611 739770 512358 851342 047295 741333 342885 382117 954686 375692 539006 595453 > 2770 [i]