Best Known (215−67, 215, s)-Nets in Base 3
(215−67, 215, 192)-Net over F3 — Constructive and digital
Digital (148, 215, 192)-net over F3, using
- 1 times m-reduction [i] based on digital (148, 216, 192)-net over F3, using
- trace code for nets [i] based on digital (4, 72, 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
- trace code for nets [i] based on digital (4, 72, 64)-net over F27, using
(215−67, 215, 419)-Net over F3 — Digital
Digital (148, 215, 419)-net over F3, using
(215−67, 215, 8140)-Net in Base 3 — Upper bound on s
There is no (148, 215, 8141)-net in base 3, because
- 1 times m-reduction [i] would yield (148, 214, 8141)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 272553 104287 315306 218683 847580 620505 950377 138949 302399 970262 957566 588276 372892 534269 277859 502721 294619 > 3214 [i]