Best Known (77−39, 77, s)-Nets in Base 3
(77−39, 77, 40)-Net over F3 — Constructive and digital
Digital (38, 77, 40)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (4, 23, 12)-net over F3, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 4 and N(F) ≥ 12, using
- net from sequence [i] based on digital (4, 11)-sequence over F3, using
- digital (15, 54, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- digital (4, 23, 12)-net over F3, using
(77−39, 77, 52)-Net over F3 — Digital
Digital (38, 77, 52)-net over F3, using
- t-expansion [i] based on digital (37, 77, 52)-net over F3, using
- net from sequence [i] based on digital (37, 51)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 37 and N(F) ≥ 52, using
- net from sequence [i] based on digital (37, 51)-sequence over F3, using
(77−39, 77, 303)-Net in Base 3 — Upper bound on s
There is no (38, 77, 304)-net in base 3, because
- 1 times m-reduction [i] would yield (38, 76, 304)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 929713 018282 994456 327637 736605 442241 > 376 [i]