Best Known (70, 70+77, s)-Nets in Base 3
(70, 70+77, 56)-Net over F3 — Constructive and digital
Digital (70, 147, 56)-net over F3, using
- 3 times m-reduction [i] based on digital (70, 150, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 55, 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 (15, 95, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 55, 28)-net over F3, using
- (u, u+v)-construction [i] based on
(70, 70+77, 82)-Net over F3 — Digital
Digital (70, 147, 82)-net over F3, using
- t-expansion [i] based on digital (69, 147, 82)-net over F3, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 69 and N(F) ≥ 82, using
- net from sequence [i] based on digital (69, 81)-sequence over F3, using
(70, 70+77, 475)-Net in Base 3 — Upper bound on s
There is no (70, 147, 476)-net in base 3, because
- 1 times m-reduction [i] would yield (70, 146, 476)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 4849 795709 764381 717027 157961 628406 297235 489910 582401 583904 551555 064553 > 3146 [i]