Best Known (86, 86+95, s)-Nets in Base 3
(86, 86+95, 61)-Net over F3 — Constructive and digital
Digital (86, 181, 61)-net over F3, using
- net from sequence [i] based on digital (86, 60)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 60)-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, 60)-sequence over F9, using
(86, 86+95, 84)-Net over F3 — Digital
Digital (86, 181, 84)-net over F3, using
- t-expansion [i] based on digital (71, 181, 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
(86, 86+95, 571)-Net in Base 3 — Upper bound on s
There is no (86, 181, 572)-net in base 3, because
- 1 times m-reduction [i] would yield (86, 180, 572)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 76 267601 304122 272294 737535 344220 819025 837528 156661 053315 515709 891587 294922 752739 938257 > 3180 [i]