Best Known (64, 141, s)-Nets in Base 3
(64, 141, 48)-Net over F3 — Constructive and digital
Digital (64, 141, 48)-net over F3, using
- t-expansion [i] based on digital (45, 141, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(64, 141, 64)-Net over F3 — Digital
Digital (64, 141, 64)-net over F3, using
- t-expansion [i] based on digital (49, 141, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(64, 141, 393)-Net in Base 3 — Upper bound on s
There is no (64, 141, 394)-net in base 3, because
- 1 times m-reduction [i] would yield (64, 140, 394)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 6 309668 979647 647326 547482 067228 202331 139084 138966 672496 353842 754605 > 3140 [i]