Best Known (162, 216, s)-Nets in Base 3
(162, 216, 328)-Net over F3 — Constructive and digital
Digital (162, 216, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 54, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
(162, 216, 905)-Net over F3 — Digital
Digital (162, 216, 905)-net over F3, using
(162, 216, 35811)-Net in Base 3 — Upper bound on s
There is no (162, 216, 35812)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 11 435882 034737 323408 301757 443627 721459 597522 422688 558141 549656 202357 837286 692560 133143 136547 021903 602417 > 3216 [i]