Best Known (63−21, 63, s)-Nets in Base 3
(63−21, 63, 84)-Net over F3 — Constructive and digital
Digital (42, 63, 84)-net over F3, using
- trace code for nets [i] based on digital (0, 21, 28)-net over F27, using
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 0 and N(F) ≥ 28, using
- the rational function field F27(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 27)-sequence over F27, using
(63−21, 63, 129)-Net over F3 — Digital
Digital (42, 63, 129)-net over F3, using
(63−21, 63, 2046)-Net in Base 3 — Upper bound on s
There is no (42, 63, 2047)-net in base 3, because
- 1 times m-reduction [i] would yield (42, 62, 2047)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 381755 460268 420998 390799 667181 > 362 [i]