Best Known (27, 42, s)-Nets in Base 3
(27, 42, 68)-Net over F3 — Constructive and digital
Digital (27, 42, 68)-net over F3, using
- trace code for nets [i] based on digital (6, 21, 34)-net over F9, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 6 and N(F) ≥ 34, using
- net from sequence [i] based on digital (6, 33)-sequence over F9, using
(27, 42, 82)-Net over F3 — Digital
Digital (27, 42, 82)-net over F3, using
(27, 42, 1046)-Net in Base 3 — Upper bound on s
There is no (27, 42, 1047)-net in base 3, because
- 1 times m-reduction [i] would yield (27, 41, 1047)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 36 574022 515730 436051 > 341 [i]