Best Known (71−47, 71, s)-Nets in Base 27
(71−47, 71, 114)-Net over F27 — Constructive and digital
Digital (24, 71, 114)-net over F27, using
- t-expansion [i] based on digital (23, 71, 114)-net over F27, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 23 and N(F) ≥ 114, using
- net from sequence [i] based on digital (23, 113)-sequence over F27, using
(71−47, 71, 160)-Net in Base 27 — Constructive
(24, 71, 160)-net in base 27, using
- 5 times m-reduction [i] based on (24, 76, 160)-net in base 27, using
- base change [i] based on digital (5, 57, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 57, 160)-net over F81, using
(71−47, 71, 208)-Net over F27 — Digital
Digital (24, 71, 208)-net over F27, using
- net from sequence [i] based on digital (24, 207)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 24 and N(F) ≥ 208, using
(71−47, 71, 8225)-Net in Base 27 — Upper bound on s
There is no (24, 71, 8226)-net in base 27, because
- 1 times m-reduction [i] would yield (24, 70, 8226)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 15690 943490 544470 035518 108653 368768 789649 752795 455121 537867 566407 457729 034383 733782 864387 921908 556153 > 2770 [i]