Best Known (134−71, 134, s)-Nets in Base 3
(134−71, 134, 52)-Net over F3 — Constructive and digital
Digital (63, 134, 52)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (13, 48, 24)-net over F3, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 13 and N(F) ≥ 24, using
- net from sequence [i] based on digital (13, 23)-sequence over F3, using
- digital (15, 86, 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 (13, 48, 24)-net over F3, using
(134−71, 134, 64)-Net over F3 — Digital
Digital (63, 134, 64)-net over F3, using
- t-expansion [i] based on digital (49, 134, 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
(134−71, 134, 418)-Net in Base 3 — Upper bound on s
There is no (63, 134, 419)-net in base 3, because
- 1 times m-reduction [i] would yield (63, 133, 419)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2928 475992 703290 821554 833148 719504 056426 154227 209105 497763 704555 > 3133 [i]