Best Known (186, 186+51, s)-Nets in Base 3
(186, 186+51, 688)-Net over F3 — Constructive and digital
Digital (186, 237, 688)-net over F3, using
- 31 times duplication [i] based on digital (185, 236, 688)-net over F3, using
- t-expansion [i] based on digital (184, 236, 688)-net over F3, using
- trace code for nets [i] based on digital (7, 59, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- trace code for nets [i] based on digital (7, 59, 172)-net over F81, using
- t-expansion [i] based on digital (184, 236, 688)-net over F3, using
(186, 186+51, 1804)-Net over F3 — Digital
Digital (186, 237, 1804)-net over F3, using
(186, 186+51, 162388)-Net in Base 3 — Upper bound on s
There is no (186, 237, 162389)-net in base 3, because
- 1 times m-reduction [i] would yield (186, 236, 162389)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 39871 010827 323088 153519 065799 776221 433134 983275 869938 752146 089932 146449 938950 119643 257716 888307 283738 582534 510283 > 3236 [i]