Best Known (76, 179, s)-Nets in Base 3
(76, 179, 51)-Net over F3 — Constructive and digital
Digital (76, 179, 51)-net over F3, using
- net from sequence [i] based on digital (76, 50)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 50)-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, 50)-sequence over F9, using
(76, 179, 84)-Net over F3 — Digital
Digital (76, 179, 84)-net over F3, using
- t-expansion [i] based on digital (71, 179, 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
(76, 179, 410)-Net in Base 3 — Upper bound on s
There is no (76, 179, 411)-net in base 3, because
- 1 times m-reduction [i] would yield (76, 178, 411)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 8 503039 042495 887564 583134 620191 311393 234516 185228 692006 442709 297492 548058 473376 462123 > 3178 [i]