Best Known (166, 235, s)-Nets in Base 4
(166, 235, 531)-Net over F4 — Constructive and digital
Digital (166, 235, 531)-net over F4, using
- t-expansion [i] based on digital (165, 235, 531)-net over F4, using
- 2 times m-reduction [i] based on digital (165, 237, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 79, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 79, 177)-net over F64, using
- 2 times m-reduction [i] based on digital (165, 237, 531)-net over F4, using
(166, 235, 1041)-Net over F4 — Digital
Digital (166, 235, 1041)-net over F4, using
(166, 235, 62769)-Net in Base 4 — Upper bound on s
There is no (166, 235, 62770)-net in base 4, because
- 1 times m-reduction [i] would yield (166, 234, 62770)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 762 211291 402481 688350 091482 602233 374051 485394 381653 921816 049070 492825 285794 553664 251572 475174 886652 586264 461861 779694 226774 753709 149664 646032 > 4234 [i]