Best Known (208−123, 208, s)-Nets in Base 3
(208−123, 208, 60)-Net over F3 — Constructive and digital
Digital (85, 208, 60)-net over F3, using
- net from sequence [i] based on digital (85, 59)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 59)-sequence over F9, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- base reduction for sequences [i] based on digital (13, 59)-sequence over F9, using
(208−123, 208, 84)-Net over F3 — Digital
Digital (85, 208, 84)-net over F3, using
- t-expansion [i] based on digital (71, 208, 84)-net over F3, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
(208−123, 208, 432)-Net in Base 3 — Upper bound on s
There is no (85, 208, 433)-net in base 3, because
- 1 times m-reduction [i] would yield (85, 207, 433)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 617 987318 458584 923600 567908 196675 656776 708592 736006 081895 540647 300627 711770 511178 754217 530520 002419 > 3207 [i]