Best Known (180−52, 180, s)-Nets in Base 3
(180−52, 180, 252)-Net over F3 — Constructive and digital
Digital (128, 180, 252)-net over F3, using
- trace code for nets [i] based on digital (8, 60, 84)-net over F27, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 8 and N(F) ≥ 84, using
- net from sequence [i] based on digital (8, 83)-sequence over F27, using
(180−52, 180, 458)-Net over F3 — Digital
Digital (128, 180, 458)-net over F3, using
(180−52, 180, 10577)-Net in Base 3 — Upper bound on s
There is no (128, 180, 10578)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 76 350845 671073 351073 180558 587686 009861 319939 615240 767101 997888 867156 575925 920869 124453 > 3180 [i]