Best Known (28, 28+19, s)-Nets in Base 3
(28, 28+19, 60)-Net over F3 — Constructive and digital
Digital (28, 47, 60)-net over F3, using
- 1 times m-reduction [i] based on digital (28, 48, 60)-net over F3, using
- trace code for nets [i] based on digital (4, 24, 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
- trace code for nets [i] based on digital (4, 24, 30)-net over F9, using
(28, 28+19, 560)-Net in Base 3 — Upper bound on s
There is no (28, 47, 561)-net in base 3, because
- 1 times m-reduction [i] would yield (28, 46, 561)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 8883 569564 088463 749187 > 346 [i]