Best Known (176, 176+57, s)-Nets in Base 3
(176, 176+57, 400)-Net over F3 — Constructive and digital
Digital (176, 233, 400)-net over F3, using
- 31 times duplication [i] based on digital (175, 232, 400)-net over F3, using
- trace code for nets [i] based on digital (1, 58, 100)-net over F81, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- net from sequence [i] based on digital (1, 99)-sequence over F81, using
- trace code for nets [i] based on digital (1, 58, 100)-net over F81, using
(176, 176+57, 1050)-Net over F3 — Digital
Digital (176, 233, 1050)-net over F3, using
(176, 176+57, 50702)-Net in Base 3 — Upper bound on s
There is no (176, 233, 50703)-net in base 3, because
- 1 times m-reduction [i] would yield (176, 232, 50703)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 492 304221 602617 385359 310734 894470 588166 946822 126568 389151 501035 774760 904652 855313 309154 008393 276951 509330 311369 > 3232 [i]