Best Known (158, 205, s)-Nets in Base 3
(158, 205, 600)-Net over F3 — Constructive and digital
Digital (158, 205, 600)-net over F3, using
- 31 times duplication [i] based on digital (157, 204, 600)-net over F3, using
- trace code for nets [i] based on digital (4, 51, 150)-net over F81, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 4 and N(F) ≥ 150, using
- net from sequence [i] based on digital (4, 149)-sequence over F81, using
- trace code for nets [i] based on digital (4, 51, 150)-net over F81, using
(158, 205, 1226)-Net over F3 — Digital
Digital (158, 205, 1226)-net over F3, using
(158, 205, 80382)-Net in Base 3 — Upper bound on s
There is no (158, 205, 80383)-net in base 3, because
- 1 times m-reduction [i] would yield (158, 204, 80383)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 21 516298 174783 795402 058404 890065 729401 026339 882107 417740 306039 606989 680697 506603 753618 237974 382547 > 3204 [i]