Best Known (85, 85+131, s)-Nets in Base 3
(85, 85+131, 60)-Net over F3 — Constructive and digital
Digital (85, 216, 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
(85, 85+131, 84)-Net over F3 — Digital
Digital (85, 216, 84)-net over F3, using
- t-expansion [i] based on digital (71, 216, 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
(85, 85+131, 412)-Net in Base 3 — Upper bound on s
There is no (85, 216, 413)-net in base 3, because
- 1 times m-reduction [i] would yield (85, 215, 413)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 3 818605 709760 275673 537639 246183 498561 269962 934800 844881 965982 642554 424760 709550 651671 511601 909844 516411 > 3215 [i]