Best Known (41, 76, s)-Nets in Base 3
(41, 76, 56)-Net over F3 — Constructive and digital
Digital (41, 76, 56)-net over F3, using
- trace code for nets [i] based on digital (3, 38, 28)-net over F9, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- the Hermitian function field over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 3 and N(F) ≥ 28, using
- net from sequence [i] based on digital (3, 27)-sequence over F9, using
(41, 76, 58)-Net over F3 — Digital
Digital (41, 76, 58)-net over F3, using
(41, 76, 440)-Net in Base 3 — Upper bound on s
There is no (41, 76, 441)-net in base 3, because
- 1 times m-reduction [i] would yield (41, 75, 441)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 615377 890790 642393 603985 507287 076915 > 375 [i]