Best Known (159, 212, s)-Nets in Base 3
(159, 212, 328)-Net over F3 — Constructive and digital
Digital (159, 212, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 53, 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
(159, 212, 891)-Net over F3 — Digital
Digital (159, 212, 891)-net over F3, using
(159, 212, 39264)-Net in Base 3 — Upper bound on s
There is no (159, 212, 39265)-net in base 3, because
- 1 times m-reduction [i] would yield (159, 211, 39265)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 47058 200639 058478 485989 066139 638969 750630 098599 860298 936301 737223 665983 306758 237291 660382 274616 028073 > 3211 [i]