Best Known (237−75, 237, s)-Nets in Base 3
(237−75, 237, 192)-Net over F3 — Constructive and digital
Digital (162, 237, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 79, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
(237−75, 237, 434)-Net over F3 — Digital
Digital (162, 237, 434)-net over F3, using
(237−75, 237, 8057)-Net in Base 3 — Upper bound on s
There is no (162, 237, 8058)-net in base 3, because
- 1 times m-reduction [i] would yield (162, 236, 8058)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 40019 149017 140792 168884 704017 000338 805742 596772 771507 126397 023739 788972 741195 504565 250813 451818 638947 324207 985549 > 3236 [i]