Best Known (27, 27+19, s)-Nets in Base 3
(27, 27+19, 60)-Net over F3 — Constructive and digital
Digital (27, 46, 60)-net over F3, using
- trace code for nets [i] based on digital (4, 23, 30)-net over F9, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 4 and N(F) ≥ 30, using
- net from sequence [i] based on digital (4, 29)-sequence over F9, using
(27, 27+19, 495)-Net in Base 3 — Upper bound on s
There is no (27, 46, 496)-net in base 3, because
- 1 times m-reduction [i] would yield (27, 45, 496)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2983 976089 968780 740321 > 345 [i]