Best Known (133−69, 133, s)-Nets in Base 3
(133−69, 133, 56)-Net over F3 — Constructive and digital
Digital (64, 133, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 49, 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, 84, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 49, 28)-net over F3, using
(133−69, 133, 64)-Net over F3 — Digital
Digital (64, 133, 64)-net over F3, using
- t-expansion [i] based on digital (49, 133, 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
(133−69, 133, 449)-Net in Base 3 — Upper bound on s
There is no (64, 133, 450)-net in base 3, because
- 1 times m-reduction [i] would yield (64, 132, 450)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1013 299138 421437 271853 669489 344259 184224 637571 056031 736284 305877 > 3132 [i]