Best Known (164−50, 164, s)-Nets in Base 3
(164−50, 164, 192)-Net over F3 — Constructive and digital
Digital (114, 164, 192)-net over F3, using
- 1 times m-reduction [i] based on digital (114, 165, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 55, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- trace code for nets [i] based on digital (4, 55, 64)-net over F27, using
(164−50, 164, 355)-Net over F3 — Digital
Digital (114, 164, 355)-net over F3, using
(164−50, 164, 6838)-Net in Base 3 — Upper bound on s
There is no (114, 164, 6839)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1 772913 013232 815423 236883 268392 305524 310665 760387 008158 446750 921022 348223 867199 > 3164 [i]