Best Known (136−71, 136, s)-Nets in Base 3
(136−71, 136, 56)-Net over F3 — Constructive and digital
Digital (65, 136, 56)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (15, 50, 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, 86, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3 (see above)
- digital (15, 50, 28)-net over F3, using
(136−71, 136, 64)-Net over F3 — Digital
Digital (65, 136, 64)-net over F3, using
- t-expansion [i] based on digital (49, 136, 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
(136−71, 136, 447)-Net in Base 3 — Upper bound on s
There is no (65, 136, 448)-net in base 3, because
- 1 times m-reduction [i] would yield (65, 135, 448)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 25876 499247 424324 637383 179339 641245 434384 128595 902400 369803 169537 > 3135 [i]